Controller and control method for internal combustion engine

ABSTRACT

To provide a controller and a control method for an internal combustion engine capable of reducing the calculation error of recirculation exhaust gas amount due to changes with time of the internal combustion engines, and humidity change of intake air, and also capable of reducing the calculation error of recirculation exhaust gas amount at transient operation. The controller and the control method for the internal combustion engine calculates humidity detecting EGR rate based on intake-air humidity and manifold humidity, calculates humidity detecting opening area which realizes humidity detecting recirculation flow rate calculated based on humidity detecting EGR rate, calculates learned opening area corresponding to present opening degree of EGR valve using learning value of opening area calculated based on humidity detecting opening area, and calculates flow rate of recirculation exhaust gas for control based on learned opening area.

INCORPORATION BY REFERENCE

The disclosure of Japanese Patent Application No. 2016-67075 filed onMar. 30, 2016 including its specification, claims and drawings, isincorporated herein by reference in its entirety.

BACKGROUND

The present invention relates to a controller and a control method foran internal combustion engine that is provided with an intake path andan exhaust path, a throttle valve for opening and closing the intakepath, an EGR path for recirculating exhaust gas from the exhaust path toan intake manifold that is part of the intake path and is at thedownstream side of the throttle valve, and an EGR valve for opening andclosing the EGR path.

In order to appropriately control an internal combustion engine, it isimportant to accurately calculate the amount of air taken into acylinder and to accurately control the fuel supply amount and theignition timing in accordance with the cylinder intake air amount.Ignition timing control needs to change an ignition timing to theignition timing (MBT: Minimum Spark Advance for Best Torque) at whichthe output torque becomes maximal or the like, in accordance with notonly the rotation speed of the internal combustion engine and thecylinder intake air amount but also other factors such as the coolanttemperature of the internal combustion engine, whether or not a knockhas occurred, the fuel property, and the EGR (Exhaust Gas Recirculation)rate.

Meanwhile, with regard to the EGR, there are two methods, i.e., a method(referred to as an external EGR, hereinafter) in which an EGR valve isprovided in an EGR path for recirculating exhaust gas from the exhaustpath to the intake manifold and the amount of exhaust gas to berecirculated to the intake manifold is controlled based on the openingdegree of the EGR valve and a method (referred to as an internal EGR,hereinafter) in which a variable valve timing mechanism, which makes theopening/closing timings of one of or both of an intake valve and anexhaust valve variable, is provided and an overlap period, during whichthe intake valve and the exhaust valve are concurrently opened, ischanged so that the amount of exhaust gas remaining in the cylinder iscontrolled. In recent years, in order to reduce the fuel cost and raisethe output, the number of internal combustion engines provided with boththe external EGR mechanism and the internal EGR mechanism has beenincreasing. In the present invention, an EGR and an EGR rate, whensimply described in this manner, denote an external EGR and an externalEGR rate, respectively.

In recent years, an internal combustion engine has been controlled byutilizing, as an index, the output torque of the internal combustionengine. Because the thermal efficiency changes depending on the cylinderintake air amount and the EGR rate, it is required to estimate theoutput torque based on the cylinder intake air amount and the EGR rate.Accordingly, either in order to control the ignition timing or in orderto estimate the output torque, it is required to accurately estimate theEGR rate.

As a technology for estimating an EGR rate, for example, thetechnologies disclosed in Japanese Patent No. 5642222 and JapaneseExamined Patent Publication No. S58-55345 have already been known. Inthe technology disclosed in Japanese Patent No. 5642222, by use of theintake air amount detected by an air flow sensor, the cylinder flowrate, which is the amount of air that flows into the cylinder and iscalculated based on the pressure in the intake manifold or the like, andthe opening degree of the EGR valve, the variation in thecharacteristics of the EGR valve and the change with time thereof arelearned so that the recirculation exhaust gas amount is estimated.

The technology disclosed in Japanese Examined Patent Publication No.S58-55345 is to perform feedback control of the opening degree of an EGRvalve so that the CO2 (carbon dioxide) concentration detected by a CO2concentration sensor provided in the intake manifold approaches a targetvalue. Japanese Examined Patent Publication No. S58-55345 also disclosesa configuration in which instead of a CO2 concentration sensor, ahumidity sensor is provided.

SUMMARY

In the technology disclosed in Japanese Patent No. 5642222, it is notrequired to add a dedicated sensor for estimating a recirculationexhaust gas amount and hence the cost hike is not caused by the increasein the number of components; however, because the recirculation exhaustgas amount is indirectly estimated, there has been a problem that anestimation error is caused by the individual differences, the changeswith time, and the like in the respective characteristics of internalcombustion engines and various kinds of sensors.

In the technology disclosed in Japanese Examined Patent Publication No.S58-55345, the recirculation exhaust gas amount is feedback-controlledbased on the humidity in the intake manifold; however, because theeffect of the humidity of intake air that is newly taken into the intakemanifold from the atmosphere, i.e., the effect of the humidity of theatmospheric air, which is provided to the humidity in the intakemanifold, is not taken into consideration, there has been a problem thatan error in controlling the recirculation exhaust gas amount is caused.Because the humidity of the atmospheric air largely changes depending onthe district, the season, the weather, and the like, the error incontrolling the recirculation exhaust gas amount exceeds the upper limitthat can be neglected.

A general humidity sensor has a response delay of time constant ofsecond order. Therefore, there has been a problem that a response delaycaused in the recirculation exhaust gas amount calculated based on theoutput signal of the humidity sensor, and the calculation error of therecirculation exhaust gas amount at the time of transient operationbecomes large.

Thus, there has been desired a controller and a control method for aninternal combustion engine capable of reducing the calculation error ofthe recirculation exhaust gas amount due to the individual differencesand the changes with time of the internal combustion engines, and thehumidity change of intake air (atmospheric air), and also capable ofreducing the calculation error of the recirculation exhaust gas amountat the time of transient operation.

According to a first aspect of the present invention, a controller foran internal combustion engine that is provided with an intake path andan exhaust path, a throttle valve for opening and closing the intakepath, an EGR path for recirculating exhaust gas from the exhaust path toan intake manifold that is part of the intake path and is at thedownstream side of the throttle valve, and an EGR valve for opening andclosing the EGR path, the internal combustion engine controllerincludes:

a driving-condition detector that detects a manifold pressure, which isa pressure of gas in the intake manifold, a manifold temperature, whichis a temperature of gas in the intake manifold, a manifold humidity,which is a humidity of gas in the intake manifold, an intake-airpressure, which is a pressure of intake air to be taken into the intakepath, an intake-air temperature, which is a temperature of the intakeair, an intake-air humidity, which is a humidity of the intake air, anintake air flow rate, which is a flow rate of the intake air, and anopening degree of the EGR valve;

a humidity detecting EGR rate calculator that calculates a humiditydetecting EGR rate, which is a ratio of a recirculation exhaust gas,which is the exhaust gas recirculated into the intake manifold, to theintake air, based on the intake-air temperature, the intake-airhumidity, the intake-air pressure, the manifold temperature, themanifold humidity, and the manifold pressure;

an opening area learning value calculator that calculates a humiditydetecting recirculation flow rate which is a flow rate of therecirculation exhaust gas based on the humidity detecting EGR rate andthe intake air flow rate, calculates a humidity detecting opening area,which is an opening area of the EGR valve which realizes the humiditydetecting recirculation flow rate, and calculates a learning value ofthe opening area of the EGR valve based on the humidity detectingopening area; and

a recirculation exhaust gas calculator for control that calculates alearned opening area of the EGR valve corresponding to the presentopening degree of the EGR valve using the learning value of the openingarea, and calculates a flow rate of the recirculation exhaust gas forcontrol used for controlling the internal combustion engine based on thelearned opening area.

According to a second aspect of the present invention, a control methodfor an internal combustion engine is a control method for an internalcombustion engine that is provided with an intake path and an exhaustpath, a throttle valve for opening and closing the intake path, an EGRpath for recirculating exhaust gas from the exhaust path to an intakemanifold that is part of the intake path and is at the downstream sideof the throttle valve, and an EGR valve for opening and closing the EGRpath, the control method includes:

a driving-condition detecting that detects a manifold pressure, which isa pressure of gas in the intake manifold, a manifold temperature, whichis a temperature of gas in the intake manifold, a manifold humidity,which is a humidity of gas in the intake manifold, an intake-airpressure, which is a pressure of intake air to be taken into the intakepath, an intake-air temperature, which is a temperature of the intakeair, an intake-air humidity, which is a humidity of the intake air, anintake air flow rate, which is a flow rate of the intake air, and anopening degree of the EGR valve;

a humidity detecting EGR rate calculating that calculates a humiditydetecting EGR rate, which is a ratio of a recirculation exhaust gas,which is the exhaust gas recirculated into the intake manifold, to theintake air, based on the intake-air temperature, the intake-airhumidity, the intake-air pressure, the manifold temperature, themanifold humidity, and the manifold pressure;

an opening area learning value calculating that calculates a humiditydetecting recirculation flow rate which is a flow rate of therecirculation exhaust gas based on the humidity detecting EGR rate andthe intake air flow rate, calculating a humidity detecting opening area,which is an opening area of the EGR valve which realizes the humiditydetecting recirculation flow rate, and calculates a learning value ofthe opening area of the EGR valve based on the humidity detectingopening area; and

a recirculation exhaust gas calculating for control that calculates alearned opening area of the EGR valve corresponding to the presentopening degree of the EGR valve using the learning value of the openingarea, and calculates a flow rate of the recirculation exhaust gas forcontrol used for controlling the internal combustion engine based on thelearned opening area.

According to the controller and the control method for the internalcombustion engine, regardless of the individual differences and thechanges with time of the internal combustion engines, and the humiditychange of intake air, the EGR rate (the humidity detecting EGR rate) canbe detected with sufficient accuracy based on the intake-air humidityand the manifold humidity. Then, based on the humidity detecting EGRrate, the learning value of the opening area of the EGR valve iscalculated. Therefore, even if it is a case where the flowcharacteristic of the EGR valve changes by deposit, such as soot, and acase where an EGR valve stops operating by aging degradation, the flowcharacteristic of the EGR valve can be learned with sufficient accuracy.Then, based on the learned opening area corresponding to the presentopening degree of the EGR valve, the flow rate of the recirculationexhaust gas for control can be calculated with good responsiveness.Therefore, while reducing the individual differences and the changeswith time of the internal combustion engines, and the humidity change ofintake air, the calculation error of the recirculation exhaust gasamount at the time of transient operation can be reduced, and thecontrol accuracy of the internal combustion engine can be improved.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic configuration diagram of an internal combustionengine and a controller according to Embodiment 1 of the presentinvention;

FIG. 2 is a block diagram of a controller according to Embodiment 1 ofthe present invention;

FIG. 3 is a hardware configuration diagram of the controller accordingto Embodiment 1 of the present invention;

FIG. 4 is a chart representing the state of partial pressures of gassesin the intake manifold according to Embodiment 1 of the presentinvention; and

FIG. 5 is a flowchart representing the processing by the controlleraccording to Embodiment 1 of the present invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS 1. Embodiment 1

A controller 50 for an internal combustion engine 1 (hereinafter,referred to simply as the controller 50) according to Embodiment 1 willbe explained with reference to the drawings. FIG. 1 is a schematicconfiguration diagram of the internal combustion engine 1 and thecontroller 50; FIG. 2 is a block diagram of the controller 50 accordingto Embodiment 1. The internal combustion engine 1 and the controller 50are mounted in a vehicle; the internal combustion engine 1 functions asa driving-force source for the vehicle (wheels).

1-1. The Configuration of the Internal Combustion Engine 1

The configuration of the internal combustion engine 1 will be explained.The internal combustion engine 1 has a cylinder 25 in which a fuel-airmixture is combusted. The internal combustion engine 1 has an intakepath 23 for supplying air to the cylinder 25 and an exhaust path 17 fordischarging exhaust gas combusted in the cylinder 25. The internalcombustion engine 1 has a throttle valve 6 for opening and closing theintake path 23. The throttle valve 6 is an electronically controlledthrottle valve that is opening/closing-driven by an electric motorcontrolled by the controller 50. The throttle valve 6 is provided with athrottle opening degree sensor 7 that generates an electric signalaccording to a throttle opening degree of the throttle valve 6.

An air cleaner 24 for purifying air taken into the intake path 23 isprovided at the most upstream portion of the intake path 23. In theintake path 23 at the upstream side of the throttle valve 6, there areprovided an air flow sensor 3 that outputs an electric signal accordingto the flow rate of intake air, which is air to be taken from theatmosphere into the intake path 23, an intake-air temperature sensor 4that outputs an electric signal according to an intake-air temperatureTa, which is the temperature of intake air, and an intake-air humiditysensor 5 that outputs an electric signal according to an intake-airhumidity Hra, which is the humidity of intake air. The pressure in theintake path 23 at the upstream side of the throttle valve 6 can beregarded as equal to the atmospheric pressure. An intake-air pressuresensor 2 that outputs an electric signal according to an intake-airpressure Pa, which is the pressure of intake air (the atmospheric air,in this example), is provided outside the intake path 23 (for example,inside the controller 50).

Each of the intake-air temperature sensor 4 and the intake-air humiditysensor 5 may be either integrated with or separated from the air flowsensor 3. Alternatively, each of the intake-air temperature sensor 4 andthe intake-air humidity sensor 5 may be provided outside the intake path23, as is the case with the intake-air pressure sensor 2; the intake-airpressure sensor 2 may be provided at a place the same as the place wherethe intake-air temperature sensor 4 and the intake-air humidity sensor 5are provided. In any case, the intake-air pressure sensor 2, theintake-air temperature sensor 4, and the intake-air humidity sensor 5are provided at a place where there exists intake air to be taken intothe intake path 23 and the pressure of the intake air is substantiallythe same.

The portion, at the downstream side of the throttle valve 6, of theintake path 23 is an intake manifold 12. The upstream portion of theintake manifold 12 is a surge tank 11 for suppressing an intake-airripple. The internal combustion engine 1 has an EGR path 21 forrecirculating exhaust gas from the exhaust path 17 to the intakemanifold 12 (the surge tank 11, in this example) and an EGR valve 22 foropening and closing the EGR path 21. The EGR valve 22 is anelectronically controlled EGR valve that is opening/closing-driven by anelectric actuator such as an electric motor to be controlled by thecontroller 50. The EGR valve 22 is provided with an EGR opening degreesensor 27 that outputs an electric signal according to the openingdegree Oe of the EGR valve 22. Exhaust gas (referred to as recirculationexhaust gas, hereinafter) that is recirculated to the surge tank 11 andintake air that is taken into the surge tank 11 are mixed andhomogenized in the surge tank 11. “EGR” is an acronym for Exhaust GasRecirculation.

In the intake manifold 12, there are provided a manifold pressure sensor8 that outputs an electric signal according to a manifold pressure Pb,which is the pressure of gas in the intake manifold 12, a manifoldtemperature sensor 9 that outputs an electric signal according to amanifold temperature Tb, which is the temperature of gas in the intakemanifold 12, and a manifold humidity sensor 10 that outputs an electricsignal according to a manifold humidity Hrb, which is the humidity ofgas in the intake manifold 12. Each of the manifold temperature sensor 9and the manifold humidity sensor 10 may be either integrated with orseparated from the manifold pressure sensor 8. The manifold temperaturesensor 9 and the manifold humidity sensor 10 are provided at thedownstream side of the connection point between the intake manifold 12and the EGR path 21 so that the temperature and the humidity of a gasobtained by sufficiently mixing intake air with recirculation exhaustgas can be detected.

An injector 13 for injecting a fuel is provided at the downstream sidepart of the intake manifold 12. The injector 13 may be provided so as toinject a fuel directly into the cylinder 25.

An ignition plug for igniting a fuel-air mixture and an ignition coil 16for supplying ignition energy to the ignition plug are provided on thetop of the cylinder 25. On the top of the cylinder 25, there areprovided an intake valve 14 for adjusting the amount of intake air to betaken from the intake path 23 into the cylinder 25 and an exhaust valve15 for adjusting the amount of exhaust gas to be exhausted from thecylinder to the exhaust path 17. The intake valve 14 is provided with anintake variable valve timing mechanism that makes the opening andclosing timing thereof variable. The exhaust valve 15 is provided withan exhaust-gas variable valve timing mechanism that makes theopening/closing timing therefor variable. Each of the variable valvetiming mechanisms 14 and 15 has an electric actuator. On the crankshaftof the internal combustion engine 1, there is provided a crank anglesensor 20 for generating an electric signal according to the rotationangle thereof.

In the exhaust path 17, there is provided an air-fuel ratio sensor 18for detecting an air-fuel (Air/Fuel) ratio AF, which is the ratio of airto fuel in exhaust gas. A catalyst 19 for purifying exhaust gas is alsoprovided in the exhaust path 17. As the catalyst 19, a three-waycatalyst, the purification performance of which becomes higher in thevicinity of the theoretical air-fuel ratio AF0, is utilized.

1-2. The Configuration of the Controller 50

Next, the controller 50 will be explained. The controller 50 is the onewhose control subject is the internal combustion engine 1. Asrepresented in FIG. 2, the controller 50 is provided with control unitssuch as a driving-condition detection unit 51, a humidity detecting EGRrate calculation unit 52, an opening area learning value calculationunit 53, a recirculation exhaust gas calculation unit for control 54,and a recirculation amount utilization control unit 55. The respectivecontrol units 51 through 55 and the like of the controller 50 arerealized by processing circuits included in the controller 50.Specifically, as illustrated in FIG. 3, the controller 50 includes, asprocessing circuits, a computing processing unit (computer) 90 such as aCPU (Central Processing Unit), storage apparatuses 91 that exchange datawith the computing processing unit 90, an input circuit 92 that inputsexternal signals to the computing processing unit 90, an output circuit93 that outputs signals from the computing processing unit 90 to theoutside, a communication circuit 94 in which the computing processingunit 90 performs data communication with external apparatuses, and thelike.

As the storage apparatuses 91, there are provided a RAM (Random AccessMemory) that can read data and write data from the computing processingunit 90, a ROM (Read Only Memory) that can read data from the computingprocessing unit 90, and the like. The input circuit 92 is connected withvarious kinds of sensors and switches and is provided with an A/Dconverter and the like for inputting output signals from the sensors andthe switches to the computing processing unit 90. The output circuit 93is connected with electric loads and is provided with a driving circuitand the like for outputting a control signal from the computingprocessing unit 90. The communication circuit 94 is connected with othervehicle electronic apparatuses such as an air conditioner controller 80,transmission controller 81, and the like through a communication wireand performs cable communication based on a communication protocol suchas the CAN (Controller Area Network).

In addition, the computing processing unit 90 runs software items(programs) stored in the storage apparatus 91 such as a ROM andcollaborates with other hardware devices in the controller 50, such asthe storage apparatus 91, the input circuit 92, the output circuit 93,and the communication circuit 94, so that the respective functions ofthe control units 51 through 55 included in the controller 50 arerealized. Setting data items such as characteristic data anddetermination values to be utilized in the control units 51 through 55are stored, as part of software items (programs), in the storageapparatus 91 such as a ROM.

In Embodiment 1, the input circuit 92 is connected with the intake-airpressure sensor 2, the air flow sensor 3, the intake-air temperaturesensor 4, the intake-air humidity sensor 5, the throttle opening degreesensor 7, the manifold pressure sensor 8, the manifold temperaturesensor 9, the manifold humidity sensor 10, the air-fuel ratio sensor 18,the crank angle sensor 20, an accelerator position sensor 26, the EGRopening degree sensor 27, and the like. The output circuit 93 isconnected with the throttle valve 6 (electric motor), the injector 13,the intake variable valve timing mechanism 14, the exhaust variablevalve timing mechanism 15, the ignition coil 16, the EGR valve 22 (theelectric actuator), and the like. The controller 50 is connected withvarious kinds of unillustrated sensors, switches, actuators, and thelike.

As basic control, the controller 50 calculates a fuel injection amount,an ignition timing, and the like, based on inputted output signals andthe like from the various kinds of sensors, and then performs drivingcontrol of the injector 13, the ignition coil 16, and the like. Based onthe output signal of the accelerator position sensor 26 and the like,the controller 50 calculates the output torque of the internalcombustion engine 1, demanded by the driver, and then controls thethrottle valve 6 and the like so that an intake air amount for realizingthe demanded output torque is obtained. In this case, the output torqueof the internal combustion engine 1 which is described below and whichis calculated based on the recirculation exhaust gas flow Qes forcontrol may be taken into consideration. Specifically, the controller 50calculates a target throttle opening degree and then performs drivingcontrol of the electric motor for the throttle valve 6 so that thethrottle opening degree, detected based on the output signal of thethrottle opening degree sensor 7, approaches the target throttle openingdegree.

<The Driving-Condition Detection Unit 51>

The driving-condition detection unit 51 detects the driving conditionsof the internal combustion engine 1 and the vehicle. Thedriving-condition detection unit 51 detects various kinds of drivingconditions, based on, for example, the output signals of various kindsof sensors. The driving-condition detection unit 51 detects a manifoldpressure Pb, a manifold temperature Tb, and a manifold humidity Hrb. InEmbodiment 1, the driving-condition detection unit 51 detects themanifold pressure Pb, based on the output signal of the manifoldpressure sensor 8. The driving-condition detection unit 51 detects themanifold temperature Tb, based on the output signal of the manifoldtemperature sensor 9. The driving-condition detection unit 51 detectsthe manifold humidity Hrb, based on the output signal of the manifoldhumidity sensor 10.

The driving-condition detection unit 51 detects an intake-air pressurePa, an intake-air temperature Ta, and an intake-air humidity Hra. InEmbodiment 1, the driving-condition detection unit 51 detects theintake-air pressure Pa, based on the output signal of the intake-airpressure sensor 2. The driving-condition detection unit 51 detects theintake-air temperature Ta, based on the output signal of the intake-airtemperature sensor 4. The driving-condition detection unit 51 detectsthe intake-air humidity Hra, based on the output signal of theintake-air humidity sensor 5.

In Embodiment 1, as each of the intake-air humidity sensor 5 and themanifold humidity sensor 10, a sensor of the type that detects arelative humidity is utilized; for example, an electric-resistor sensorthat detects a relative humidity based on the electric resistance valueof a moisture-sensitive material, an electrostatic-capacitance sensorthat detects a relative humidity based on the electrostatic capacitanceof a sensor element, or the like is utilized. Accordingly, thedriving-condition detection unit 51 detects a relative humidity, as eachof the manifold humidity Hrb and the intake-air humidity Hra. Thehumidity sensors 5 and 10 have a response delay of the time constant forabout several seconds.

The driving-condition detection unit 51 detects a throttle openingangle, based on the output signal of the throttle position sensor 7, anddetects the opening degree Oe of the EGR valve 22, based on the outputsignal of the EGR opening degree sensor 27. The driving-conditiondetection unit 51 detects an air-fuel ratio AF of the exhaust gas, basedon the output signal of the air-fuel ratio sensor 18, detects arotational speed Ne of the internal combustion engine 1, based on theoutput signal of the crank angle sensor 20, and detects an acceleratoropening degree, based on the output signal of the accelerator positionsensor 26.

The driving-condition detection unit 51 detects the intake air flowrates Qa, based on the output signal of the air flow sensors 3. Thedriving-condition detection unit 51 calculates an intake air amount QA[g/stroke] taken into the intake path 23 (intake manifold 12) in onestroke period (for example, the interval of BTDC5degCA) based on theintake air flow rate Qa [g/s], as shown in an equation (1); and appliesfirst-order-lag filtering processing, which simulates a delay in theintake manifold 12 (surge tank), to the intake air amount QA, so as tocalculate a cylinder intake air amount QAc [g/stroke] taken into thecylinder 25 in one stroke period. The driving-condition detection unit51 calculates the intake air amount QA by multiplying one stroke periodΔT to the intake air flow rate Qa, for example.QAc(n)=KCCA·QAc(n−1)+(1−KCCA)·QA(n)QA(n)=Qa(n)·ΔT(n)  (1)

Where KCCA is a preliminarily set filter gain. Where (n) denotes thevalue in the present calculation cycle, and (n−1) denotes the value inthe immediately previous calculation cycle.

The driving-condition detection unit 51 calculates a charging efficiencyEc of intake air by dividing the cylinder intake air amount QAc by avalue obtained by multiplying the density ρ0 of air under the standardatmospheric condition to the cylinder volume Vc. The charging efficiencyEc is the ratio of the cylinder intake air amount QAc to the mass(ρ0×Vc) of air under the standard atmospheric condition, with which thecylinder volume Vc is filled. The standard atmospheric condition denotesthe state of 1 atm and 25° C.

$\begin{matrix}{{Ec} = \frac{QAc}{\rho\;{0 \cdot {Vc}}}} & (2)\end{matrix}$

The driving-condition detection unit 51 detects a temperature Tex of theexhaust gas at the exhaust path 17 side of the EGR valve 22. InEmbodiment 1, the driving-condition detection unit 51 calculates thetemperature Tex of the exhaust gas corresponding to the presentrotational speed Ne of the internal combustion engine 1 and the presentcharging efficiency Ec, by use of an exhaust gas temperaturecharacteristic data in which the relationship among the rotational speedNe of the internal combustion engine 1, the charging efficiency Ec, andthe temperature Tex of the exhaust gas. A temperature sensor may beprovided in the exhaust path 17, and the driving-condition detectionunit 51 may detect the temperature Tex of the exhaust gas based on theoutput signal of the temperature sensor. A data map, a data table, apolynomial, an equation, and the like are used for each characteristicdata.

The driving-condition detection unit 51 detects a pressure Pex of theexhaust gas at the exhaust path 17 side of the EGR valve 22. InEmbodiment 1, the driving-condition detection unit 51 calculates thepressure Pex of the exhaust gas corresponding to the present rotationalspeed Ne of the internal combustion engine 1 and the present chargingefficiency Ec, by use of an exhaust gas pressure characteristic data inwhich the relationship among the rotational speed Ne of the internalcombustion engine 1, the charging efficiency Ec, and the pressure Pex ofexhaust gas.

<The Humidity Detecting EGR Rate Calculation Unit 52>

The humidity detecting EGR rate calculation unit 52 calculates ahumidity detecting EGR rate Regr, which is a ratio of the recirculatedexhaust gas, which is the exhaust gas recirculated into the intakemanifold 12, to the intake air, based on the intake-air temperature Ta,the intake-air humidity Hra, the intake-air pressure Pa, the manifoldtemperature Tb, the manifold humidity Hrb, and the manifold pressure Pb.The detail of the humidity detecting EGR rate calculation unit 52 willbe described later.

<The Opening Area Learning Value Calculation Unit 53>

The opening area learning value calculation unit 53 is provided with ahumidity detecting recirculation flow rate calculation unit 56 thatcalculates a humidity detecting recirculation flow rate Qeh, which is aflow rate of the recirculation exhaust gas, based on the humiditydetecting EGR rate Regr and the intake air flow rate Qa. In Embodiment1, the humidity detecting EGR rate Regr calculated by the humiditydetecting EGR rate calculation unit 52 is an absolute EGR rate which isa ratio of the recirculation exhaust gas to the sum of the intake airand the recirculation exhaust gas, as shown in the equation (11)described later. Then, as shown in an equation (3), the humiditydetecting recirculation flow rate calculation unit 56 converts theabsolute EGR rate Regr into a relative EGR rate Regrr which is a ratioof the recirculation exhaust gas to the intake air, and then calculatesa humidity detecting recirculation flow rate Qeh by multiplying theintake air flow rate Qa to the relative EGR rate Regrr.

$\begin{matrix}{{{{Re}\;{grr}} = \frac{Regr}{1 - {Regr}}}{{Qeh} = {{Re}\;{{grr} \cdot {Qa}}}}} & (3)\end{matrix}$

The opening area learning value calculation unit 53 is provided with ahumidity detecting opening area calculation unit 57 that calculates ahumidity detecting opening area Segrh which is an opening area of theEGR valve 22 which realizes the humidity detecting recirculation flowrate Qeh, and a learning value calculation unit 58 that calculates alearning value ΔSegrL of the opening area of the EGR valve 22 based onthe humidity detecting opening area Segrh.

In Embodiment 1, the humidity detecting opening area calculation unit 57calculates a sonic velocity Ae of the exhaust gas at the exhaust path 17side of the EGR valve 22 based on the temperature Tex of the exhaustgas. The humidity detecting opening area calculation unit 57 calculatesa density ρe of the exhaust gas at the exhaust path 17 side of the EGRvalve 22 based on the temperature Tex of the exhaust gas and thepressure Pex of the exhaust gas. Then, the humidity detecting openingarea calculation unit 57 calculates the humidity detecting opening areaSegrh based on the manifold pressure Pb, the pressure Pex of the exhaustgas, the sonic velocity Ae of the exhaust gas, the density ρe of theexhaust gas, and the humidity detecting recirculation flow rate Qeh.

Specifically, the humidity detecting opening area calculation unit 57calculates the humidity detecting opening area Segrh which realizes thehumidity detecting recirculation flow rate Qeh, by use of an orificeflow rate calculation equation which is a fluid-mechanics theoreticalformula for a compressible fluid, in which the flow in the vicinity ofthe EGR valve 22 is regarded as flows before and after a throttle valve.The theoretical formula for the flow rate Qe [g/s] of the recirculationexhaust gas that flows through the EGR valve 22, regarded as a throttlevalve, is derived as represented in the equation (4), from the energyconservation law, the isentropic flow relational equation, the sonicvelocity relational equation, and the state equation.

$\begin{matrix}{{{Qe} = {{{Ae} \cdot \rho}\;{e \cdot {Segr} \cdot \sigma}\; e}}{{{Ae} = \sqrt{\kappa \cdot R \cdot {Tex}}},{{\rho\; e} = \frac{Pex}{R \cdot {Tex}}}}{{\sigma\; e} = \sqrt{\frac{2}{\kappa - 1}\left\lbrack {\left( \frac{Pb}{Pex} \right)^{\frac{2}{\kappa}} - \left( \frac{Pb}{Pex} \right)^{\frac{\kappa + 1}{\kappa}}} \right\rbrack}}} & (4)\end{matrix}$

Where κ is a specific heat ratio of the recirculation exhaust gas, and apreliminarily set value is used. R is a gas constant of therecirculation exhaust gas, and a preliminarily set value is used. Segris an opening area of the EGR valve 22. σe is a dimensionless flow rateconstant that varies in accordance with a pressure ratio Pb/Pex of theflow at downstream side of (after) the EGR valve 22 to the flow at theupstream side of (before) the EGR valve 22.

The humidity detecting opening area calculation unit 57 calculates asonic velocity Ae of the exhaust gas based on the temperature Tex of theexhaust gas by use of the second equation of the equation (4). Thehumidity detecting opening area calculation unit 57 calculates a densityρe of the exhaust gas based on the temperature Tex of the exhaust gasand the pressure Pex of the exhaust gas by use of the third equation ofthe equation (4).

The humidity detecting opening area calculation unit 57 calculates thedimensionless flow rate constant σe corresponding to the presentpressure ratio Pb/Pex of the pressure Pex of the exhaust gas and themanifold pressure Pb, by use of a flow rate constant characteristic datain which the relationship between the pressure ratio Pb/Pex of thepressure Pex of the exhaust gas and the manifold pressure Pb, and thedimensionless flow rate constant σe is preliminarily set based on thefourth equation of the equation (4).

Then, as shown in the equation (5) which is obtained by rearranging thefirst equation of the equation (4) with regard to the opening area Segr,the humidity detecting opening area calculation unit 57 calculates thehumidity detecting opening area Segrh by dividing the humidity detectingrecirculation flow rate Qeh by the sonic velocity Ae, the density ρe,and the dimensionless flow rate constant σe of the exhaust gas.

$\begin{matrix}{{Segrh} = \frac{Qeh}{{{Ae} \cdot \rho}\;{e \cdot \sigma}\; e}} & (5)\end{matrix}$

The learning value calculation unit 58 calculates a base opening areaSegrb corresponding to the present opening degree Oe of the EGR valve22, by use of a base opening characteristic data in which therelationship between the base opening area Segrb of the EGR valve 22 andthe opening degree Oe of the EGR valve 22 is preliminarily set. Then,the learning value calculation unit 58 calculates a learning valueΔSegrL of opening area, based on the comparison result between the baseopening area Segrb and the humidity detecting opening area Segrh.

In Embodiment 1, as shown in the equation (6), the learning valuecalculation unit 58 calculates a difference ΔSegrh of opening areabetween the humidity detecting opening area Segrh and the base openingarea Segrb; calculates a value obtained by applying an averagingprocessing (in this example, a first-order-lag filtering processing) tothe difference ΔSegrh of opening area as the learning value ΔSegrL ofopening area; and stores the learning value ΔSegrL to the storageapparatus 91 such as nonvolatile RAM.ΔSegrh(n)=Segrh(n)−Segrb(n)ΔSegrL(n)=Ks·ΔSegrL(n−1)+(1−Ks)·ΔSegrh(n)  (6)Where (n) denotes the value in the present calculation cycle, and (n−1)denotes the value in the immediately previous calculation cycle. Ksdenotes a filter gain in the first-order lag filtering processing and ispreliminarily set to a value corresponding to the time constant.Averaging processing, such as a moving-averaging processing, may beperformed instead of the first order lag filtering processing, forexample. A ratio of opening area and the like may be used instead of thedifference ΔSegrh of opening area.

The averaging processing can reduce the influence of the response delayof the manifold humidity sensor 10, the response deviation between thehumidity detecting recirculation flow rate Qeh and the flow rate of therecirculation exhaust gas which passes the EGR valve 22 because thehumidity detecting EGR rate Regr is an EGR rate after mixing in theintake manifold 12, other disturbance factors, and the like; andstability and accuracy of the learning value ΔSegrL of opening area canbe improved.

Alternatively, the learning value calculation unit 58 may increase ordecrease the learning value ΔSegrL of opening area, based on thecomparison result between the humidity detecting opening area Segrh andthe learned opening area SegrL described later. For example, thelearning value calculation unit 58 increases the learning value ΔSegrLof opening area, in the case where the humidity detecting opening areaSegrh is larger than the learned opening area SegrL; and the learningvalue calculation unit 58 decreases the learning value ΔSegrL of openingarea, in the case where the humidity detecting opening area Segrh issmaller than the learned opening area SegrL.

The learning value calculation unit 58 may calculate the learning valueΔSegrL of opening area for each operating point of the opening degree Oeof the EGR valve 22. For example, the learning value calculation unit 58stores the learning value ΔSegrL of opening area to the storageapparatus 91, such as nonvolatile RAM, for each opening degree sectionwhere the opening degree Oe of the EGR valve 22 was preliminarilydivided into a plurality of sections; then the learning valuecalculation unit 58 reads out the learning value ΔSegrL of the openingdegree section corresponding to the present opening degree Oe of the EGRvalve 22 from the storage apparatus 91, and updates the learning valueΔSegrL by the difference ΔSegrh of opening area. Accordingly, the samenumber of the learning value ΔSegrL of opening area as the number of theopening degree section is provided.

The learning value calculation unit 58 permits a update of the learningvalue ΔSegrL of opening area using the equation (6) in the case ofdetermining that a change of the EGR rate is small and in a steadystate; and the learning value calculation unit 58 prohibits the updateof the learning value ΔSegrL of opening area using the equation (6) andholds the learning value ΔSegrL of opening area in the case ofdetermining that the change of the EGR rate is large and in a transientstate. For example, in the case where a period, in which a change amountof the opening degree Oe of the EGR valve 22 is less than or equal to apreliminarily set EGR determination value and a change amount of theopening degree of the throttle valve 6 is less than or equal to apreliminarily set throttle determination value, passes a preliminarilyset decision period, the learning value calculation unit 58 determinesthat the change of the EGR rate is in the steady state; otherwise, thelearning value calculation unit 58 determines that the change of the EGRrate is in the transient state.

Such learning permission conditions can reduce the influence of theresponse delay of the manifold humidity sensor 10, the responsedeviation between the humidity detecting recirculation flow rate Qeh andthe flow rate of the recirculation exhaust gas which passes the EGRvalve 22 because the humidity detecting EGR rate Regr is an EGR rateafter mixing in the intake manifold 12, and the like; and accuracy ofthe learning value ΔSegrL of opening area can be improved.

<The Recirculation Exhaust Gas Calculation Unit for Control 54>

The recirculation exhaust gas calculation unit for control 54 isprovided with a learned opening area calculation unit 59 that calculatesa learned opening area SegrL of the EGR valve 22 corresponding to thepresent opening degree Oe of the EGR valve 22 using the learning valueΔSegrL of opening area, and a recirculation flow rate calculation unit60 for control that calculates a flow rate Qes of the recirculationexhaust gas for control used for control of the internal combustionengine 1 based on the learned opening area SegrL.

Since the humidity detecting recirculation flow rate Qeh which isdelayed in a response due to the response delay of the humidity sensoris not used directly, but the learning value ΔSegrL of opening areacalculated based on the humidity detecting recirculation flow rate Qehis used, while suppressing that a response delay due to the humiditysensor causes in the flow rate Qes of the recirculation exhaust gas forcontrol, the calculation accuracy of the flow rate Qes of therecirculation exhaust gas for control can be enhanced.

In Embodiment 1, the learned opening area calculation unit 59 calculatesthe learned opening area SegrL by correcting the base opening area Segrbby the learning value ΔSegrL of opening area. Then, the recirculationflow rate calculation unit 60 for control calculates the flow rate Qesof the recirculation exhaust gas for control, based on the learnedopening area SegrL, the manifold pressure Pb, the pressure Pex of theexhaust gas, the sonic velocity Ae of the exhaust gas, and the densityρe of the exhaust gas.

The learned opening area calculation unit 59 calculates a value obtainedby adding the learning value ΔSegrL of opening area to the base openingarea Segrb corresponding to the present opening degree Oe of the EGRvalve 22, as the learned opening area SegrL, as shown in the equation(7). As is the case with the learning value calculation unit 58, thelearned opening area calculation unit 59 calculates the base openingarea Segrb corresponding to the present opening degree Oe of the EGRvalve 22 by use of the base opening characteristic data described above.The base opening area Segrb which the learning value calculation unit 58calculated may be used.SegL=Segrb+ΔSegrL  (7)

In the case where the opening area learning value calculation unit 53 isconfigured to calculate the learning value ΔSegrL of opening area foreach operating point of the opening degree Oe of the EGR valve 22, thelearned opening area calculation unit 59 calculates the flow rate Qes ofthe recirculation exhaust gas for control using the learning valueΔSegrL of opening area corresponding to the present opening degree Oe ofthe EGR valve 22. Specifically, the learned opening area calculationunit 59 reads out the learning value ΔSegrL of opening degree sectioncorresponding to the present opening degree Oe of the EGR valve 22 fromthe storage apparatus 91, and calculates a value obtained by adding theread learning value ΔSegrL to the base opening area Segrb, as thelearned opening area SegrL.

The recirculation flow rate calculation unit for control 60 calculatesthe flow rate Qes of the recirculation exhaust gas for control realizedby the learned opening area SegrL by use of the orifice flow ratecalculation equation of the equation (4), as is the case with theopening area learning value calculation unit 53. As is the case with thehumidity detecting opening area calculation unit 57, the recirculationflow rate calculation unit for control 60 calculates the sonic velocityAe of the exhaust gas based on the temperature Tex of the exhaust gas byuse of the second equation of the equation (4). As is the case with thehumidity detecting opening area calculation unit 57, the recirculationflow rate calculation unit for control 60 calculates the density ρe ofthe exhaust gas based on the temperature Tex of the exhaust gas and thepressure Pex of the exhaust gas by use of the third equation of theequation (4). As is the case with the humidity detecting opening areacalculation unit 57, the recirculation flow rate calculation unit forcontrol 60 calculates the dimensionless flow rate constant σecorresponding to the present pressure ratio Pb/Pex of the pressure Pexof the exhaust gas and the manifold pressure Pb, by use of the flow rateconstant characteristic data described above. The sonic velocity Ae ofthe exhaust gas, the density ρe of the exhaust gas, and thedimensionless flow rate constant σe, which the humidity detectingopening area calculation unit 57 calculated, may be used.

Then, the recirculation flow rate calculation unit for control 60calculates a value obtained by multiplying the sonic velocity Ae, thedensity ρe, and the dimensionless flow rate constant σe of the exhaustgas to the learned opening area SegrL, as the flow rate Qes of therecirculation exhaust gas for control, by use of the equation (8)corresponding to the first equation of the equation (4).Qes=Ae·ρe·SegrL·σe  (8)

The recirculation exhaust gas calculation unit for control 54 isprovided with an EGR rate calculation unit for control 61 thatcalculates an EGR rate Regrs for control based on the flow rate Qes ofthe recirculation exhaust gas for control. The EGR rate calculation unitfor control 61 calculates a recirculation exhaust gas amount QES[g/stroke] which recirculates to the intake manifold 12 in one strokeperiod (for example, the interval of BTDC5degCA) based on the flow rateQes [g/s] of the recirculation exhaust gas for control, as shown in theequation (9); and applies first-order-lag filtering processing, whichsimulates a delay in the intake manifold 12 (surge tank), to therecirculation exhaust gas amount QES, so as to calculate a cylinderintake recirculation exhaust gas amount QESc [g/stroke] which is anamount of the recirculation exhaust gas taken into the cylinder 25 inone stroke period. The EGR rate calculation unit for control 61calculates the recirculation exhaust gas amount QES by multiplying onestroke period ΔT to the flow rate Qes [g/s] of the recirculation exhaustgas for control, for example.QESc(n)=KCCA·QESc(n−1)+(1−KCCA)·QES(n)QES(n)=Qes(n)·ΔT(n)  (9)

Where KCCA is the preliminarily set filter gain, and the same value asone of the equation (1) can be used.

The EGR rate calculation unit for control 61 calculates the EGR rateRegrs for control based on the cylinder intake air amount QAc and thecylinder intake recirculation exhaust gas amount QESc. In Embodiment 1,as shown in the equation (10), the EGR rate calculation unit for control61 calculates, as the EGR rate Regrs for control, a relative EGR ratewhich divided the cylinder intake recirculation exhaust gas amount QEScby the cylinder intake air amount QAc. An absolute EGR rate may becalculated.

$\begin{matrix}{{{Re}\;{grs}} = \frac{QESc}{QAc}} & (10)\end{matrix}$<Recirculation Amount Utilization Control Unit 55>

The recirculation amount utilization control unit 55 controls theinternal combustion engine 1 using the recirculation exhaust gas flowrate Qes for control which is calculated by the recirculation exhaustgas calculation unit for control 54. In Embodiment 1, the recirculationamount utilization control unit 55 performs at least one or more of achange of the ignition timing, a change of the opening degree Oe of theEGR valve 22, and a calculation of an output torque of the internalcombustion engine 1, based on the flow rate Qes of the recirculationexhaust gas for control.

For example, the recirculation amount utilization control units 55calculates the ignition timing, based on the rotation speed Ne of theinternal combustion engine 1, the charging efficiency Ec, and the EGRrate Regrs for control. The recirculation amount utilization controlunit 55 calculates a target EGR rate based on driving condition such asthe rotational speed Ne of the internal combustion engine 1 and thecharging efficiency Ec, and increases or decreases the opening degree Oeof the EGR valve 22 so that the EGR rate Regrs for control approachesthe target EGR rate. By improving the calculation accuracy of therecirculation exhaust gas flow rate Qes for control, the settingprecision of the ignition timing and the control accuracy of the EGRrate can be improved, and the control accuracy of the combustioncondition, the output torque, the thermal efficiency, the NOx generationamount, and the like of the internal combustion engine 1 can beimproved.

The recirculation amount utilization control units 55 calculates thethermal efficiency, based on the rotation speed Ne of the internalcombustion engine 1, the charging efficiency Ec, and the EGR rate Regrsfor control. Then, the recirculation amount utilization control unit 55calculates an indicated mean effective pressure by multiplying thethermal efficiency to the calorific value of the fuel supplied to thecylinder 25, and calculates the output torque of the internal combustionengine 1 based on the indicated mean effective pressure. Therecirculation amount utilization control unit 55 changes the ignitiontiming, the intake air amount, and the recirculation exhaust gas amountbased on the output torque of the internal combustion engine 1, ortransmits the output torque of the internal combustion engine 1 to othercontrollers such as the transmission controller 81 and makes othercontrollers use the output torque for a torque control of the wholevehicle.

1-2-1. Detailed Explanation of the Humidity Detecting EGR RateCalculation Unit 52

Next, the humidity detecting EGR rate calculation unit 52 is explainedin detail.

1-2-1-1. Theoretical Derivation of the Calculation Method for theHumidity Detecting EGR Rate Regr

At first, theoretical derivation of a calculation method for thehumidity detecting EGR rate Regr will be explained. In Embodiment 1, thehumidity detecting EGR rate Regr is the absolute EGR rate, and is theratio of the exhaust gas (recirculation exhaust gas) recirculated intothe intake manifold 12 to the gas in the intake manifold 12. In thefollowing description, the humidity detecting EGR rate Regr also bereferred to simply as the EGR rate Regr. By use of the equation (11),the EGR rate Regr can be calculated based on the CO2 concentration.

$\begin{matrix}{{Regr} = \frac{{CO}_{2{\_ in}} - {CO}_{2{\_ a}}}{{CO}_{2{\_ ex}} - {CO}_{2{\_ a}}}} & (11)\end{matrix}$

Where CO2_in is the concentration [vol %] of CO2 in the gas inside theintake manifold 12; CO2_ex is the concentration [vol %] of CO2 in theexhaust gas inside the exhaust path 17; CO2_a is the concentration [vol%] of CO2 in the intake air. In general, the concentration of CO2 in theintake air (the atmospheric air) is approximately 0.038 [vol %].

Hereinafter, by paying attention to the respective numbers of moles ofmolecules and the partial pressures of gases in a combustion chemicalreaction formula, a relational equation among the respective numbers ofmoles of molecules, the partial pressures, the CO2 concentration, andthe EGR rate Regr will be derived. The combustion chemical reactionformula for a hydrocarbon at a time when the fuel of the internalcombustion engine 1 is gasoline, for example, is expressed by theequation (12).

$\begin{matrix}{\left. {{C_{n}H_{m}} + {\left( {n + \frac{m}{4}} \right) \cdot O_{2}}}\rightarrow{{n \cdot {CO}_{2}} + {{\frac{m}{2} \cdot H_{2}}O}} \right.~} & (12)\end{matrix}$

In the case where when it is assumed that the average molecular formulafor gasoline is C7H14 and that the composition of air is “oxygen (O2):nitrogen (N2)=21:79”, the gasoline and the air combust together at thetheoretical air-fuel ratio AF0, the combustion chemical reaction formulais expressed by the equation (13). In the equation (13), the respectivenumbers of moles of carbon dioxide (CO2) and water vapor (H2O), whichare produced by the combustion, are the same, i.e., 14.2.C₇H₁₄+21.O₂+79.N₂→14.CO₂+14.H₂O+79.N₂  (13)

However, actual intake air includes carbon dioxide (CO2) and water vapor(H2O); thus, when it is assumed that the respective numbers of moles ofcarbon dioxide (CO2) and water vapor (H2O) are α and β, the combustionchemical reaction formula is expressed by the equation (14). Theequation (14) is a pure combustion chemical reaction formula in which norecirculation exhaust gas is taken into consideration.2.C₇H₁₄+21.O₂+79.N₂+α.CO₂+β.H₂O→(14+α).CO₂+(14+β).H₂O+79.N₂  (14)

In the following analysis of the number of moles, the number of moles ofgasoline in the left-hand side of the equation (14) is approximated with“0” because it is small in comparison with the number of total moles.Accordingly, the pre-combustion gas represented in the left-hand side ofthe equation (14) becomes equal to the intake air. Because the number oftotal moles of the intake air represented in the left-hand side of theequation (14) is (100+α+β) and the number of total moles of the exhaustgas represented in the right-hand side of the equation (14) is(107+α+β), the respective numbers of moles at the left-hand side and atthe right-hand side are different from each other, strictly speaking;however, in this example, it is assumed that both the respective numbersof total moles at the left-hand side and at the right-hand side are(M+α+β).

FIG. 4 represents the state of partial pressures of gasses in the intakemanifold 12 at a time when exhaust gas is recirculated to the intakemanifold 12. The gas in the intake manifold 12 is a mixture gasincluding intake air taken from the atmosphere and recirculation exhaustgas recirculated through the EGR path 21; the partial pressure of theintake air in the manifold pressure is expressed by “P_new”, and thepartial pressure of the recirculation exhaust gas is expressed by“P_egr”.

As represented in the left-hand side of the equation (14), the intakeair is composed of nitrogen (N2), oxygen (O2), carbon dioxide (CO2), andwater vapor (H2O). Strictly speaking, although included in the intakeair, other substances are neglected because their content is extremelysmall. Pvn denotes the partial pressure of water vapor included in theintake air.

As represented in the right-hand side of the equation (14), therecirculation exhaust gas is composed of nitrogen (N2), carbon dioxide(CO2), and water vapor (H2O). Strictly speaking, although included inthe intake air, other substances are neglected because their content isextremely small. The carbon dioxide (CO2) includes carbon dioxide (CO2)that is produced through combustion and carbon dioxide (CO2) that hasoriginally been included in the intake air; the water vapor (H2O)includes water vapor (H2O) that is produced through combustion and watervapor (H2O) that has originally been included in the intake air.Accordingly, the partial pressure of the water vapor produced throughcombustion is expressed by Pve, and the partial pressure of the watervapor that has originally been included in the intake air is expressedby Pvr.

When the respective CO2 concentrations in the equation (11) forcalculating the EGR rate Regr are expressed by the respective ratios ofthe partial pressure P_new of the intake air and the partial pressureP_egr of the recirculation exhaust gas to the manifold pressure Pb,represented in FIG. 4, and the mole fraction of CO2 in the intake airrepresented in the left-hand side of the equation (14) or in the exhaustgas represented in the right-hand side of the equation (14), theequation (15) is yielded. Specifically, as represented in FIG. 4, theconcentration CO2_in of CO2 in the gas inside the intake manifold 12 isthe total of the concentration of CO2 in the intake air inside theintake manifold 12, the concentration of CO2 that is produced throughcombustion and included in the recirculation exhaust gas, and theconcentration of CO2 included in the intake air. The concentration ofCO2 in the intake air inside the intake manifold 12 is obtained bymultiplying the ratio of the partial pressure P_new of the intake air tothe manifold pressure Pb by the mole fraction (α/(M+α+β)) of CO2 in theintake air, represented in the left-hand side of the equation (14). Theconcentration of CO2 produced through combustion and CO2 in the intakeair that are included in the recirculation exhaust gas is obtained bymultiplying the ratio of the partial pressure P_egr of the recirculationexhaust gas to the manifold pressure Pb by the mole fraction((14+α)/(M+α+β)) of CO2 in the exhaust gas, represented in theright-hand side of the equation (14). The concentration CO2_ex of CO2 inthe exhaust gas is the mole fraction ((14+α)/(M+α+β)) of CO2 in theexhaust gas, represented in the right-hand side of the equation (14).The concentration CO2_a of CO2 in the intake air is the mole fraction(α/(M+α+β)) of CO2 in the intake air, represented in the left-hand sideof the equation (14).

$\begin{matrix}{{{CO}_{2{\_ in}} = {{\frac{P\_ new}{Pb} \cdot \frac{\alpha}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot \frac{14 + \alpha}{M + \alpha + \beta}}}}{{CO}_{2{\_ ex}} = \frac{14 + \alpha}{M + \alpha + \beta}}{{CO}_{2{\_ a}} = \frac{\alpha}{M + \alpha + \beta}}} & (15)\end{matrix}$

When the respective concentrations of CO2 in the equation (15) aresubstituted for the equation (11) and the equation (1) is rearranged,the EGR rate Regr is given by the ratio (P_egr/Pb) of the partialpressure P_egr of the recirculation exhaust gas to the manifold pressurePb, as represented in the equation (16).

$\begin{matrix}\begin{matrix}{{Regr} = {\frac{{CO}_{2{\_ in}} - {CO}_{2{\_ a}}}{{CO}_{2{\_ ex}} - {CO}_{2{\_ a}}} = \frac{\begin{matrix}\left( {{\frac{P\_ new}{Pb} \cdot \frac{\alpha}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot}} \right. \\{\left. \frac{14 + \alpha}{M + \alpha + \beta} \right) - \left( \frac{\alpha}{M + \alpha + \beta} \right)}\end{matrix}}{\left( \frac{14 + \alpha}{M + \alpha + \beta} \right) - \left( \frac{\alpha}{M + \alpha + \beta} \right)}}} \\{= \frac{P\_ egr}{Pb}}\end{matrix} & (16)\end{matrix}$

Next, a relational equation will be derived by paying attention to themole fractions of the gases. By use of the mole fraction (β/(M+α+β)) ofwater vapor in the intake air represented in the left-hand side of theequation (14), the mole fraction χva of the water vapor in the intakeair can be expressed as in the equation (17).

$\begin{matrix}{{\chi\;{va}} = \frac{\beta}{M + \alpha + \beta}} & (17)\end{matrix}$

As represented in FIG. 4 and the equation (18), the mole fraction χvb ofthe water vapor in the gas inside the intake manifold 12 is the total ofthe mole fraction (the first item in the right-hand side of the equation(18)) of the water vapor included in the intake air inside the intakemanifold 12 and the mole fraction (the second item in the right-handside of the equation (18)) of the water vapor produced throughcombustion and the water vapor in the intake air, which are included inthe recirculation exhaust gas. As represented in the first item of theright-hand side of the equation (18), the mole fraction of the watervapor included in the intake air inside the intake manifold 12 isobtained by multiplying the ratio (P_new/Pb) of the partial pressureP_new of the intake air to the manifold pressure Pb by the mole fraction(β/(M+α+β)) of the water vapor in the intake air, represented in theleft-hand side of the equation (14). As represented in the second itemof the right-hand side of the equation (18), the mole fraction of thewater vapor included in the intake air and the water vapor producedthrough combustion, which are included in the recirculation exhaust gas,is obtained by multiplying the ratio (P_egr/Pb) of the partial pressureP_egr of the recirculation exhaust gas to the manifold pressure Pb bythe mole fraction ((14+β/(M+α+β)) of the water vapor in the exhaust gas,represented in the right-hand side of the equation (14). Accordingly,the mole fraction χvb of the water vapor in the intake manifold 12 canbe expressed as in the equation (18), by use of these mole fractions ofwater vapor.

$\begin{matrix}\begin{matrix}{{\chi\;{vb}} = {{\frac{P\_ new}{Pb} \cdot \frac{\beta}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot \frac{14 + \beta}{M + \alpha + \beta}}}} \\{= {\frac{\beta}{M + \alpha + \beta} + {\frac{P\_ egr}{Pb} \cdot \frac{14}{M + \alpha + \beta}}}}\end{matrix} & (18)\end{matrix}$

The rearranged first item (β/(M+α+β)) of the right-hand side of theequation (18) is equal to the mole fraction χva of the water vapor inthe intake air, represented in the equation (17); thus, when theequation (17) is substituted for the equation (18) and then the equation(18) is rearranged, the equation (19) is obtained. As represented in theequation (19), the subtraction mole fraction (χvb−χva) obtained bysubtracting the mole fraction χva of the water vapor in the intake airfrom the mole fraction χvb of the water vapor in the intake manifold 12is equal to the value obtained by multiplying the ratio (P_egr/Pb) ofthe partial pressure P_egr of the recirculation exhaust gas to themanifold pressure Pb by the mole fraction χvex (=14/(M+α+β)) ofinner-exhaust-gas combustion-produced water vapor, which is the molefraction of water vapor produced through combustion in the exhaust gas,obtained from the right-hand side of the equation (14). The subtractionmole fraction (χvb−χva) becomes equal to the mole fraction χvegr of thewater vapor, produced through combustion, in the recirculation exhaustgas (referred to as the mole fraction χvegr of combustion-produced watervapor in the intake manifold 12). Thus, the equation (19) suggests thatthe mole fraction χvegr of combustion-produced water vapor in the intakemanifold 12 is equal to a multiplication value obtained by multiplyingthe ratio (P_egr/Pb) of the partial pressure P_egr of the recirculationexhaust gas to the manifold pressure Pb by the mole fraction χvex ofinner-exhaust-gas combustion-produced water vapor.

$\begin{matrix}{{{\chi\;{vb}} - {\chi\;{va}}} = {{\frac{P\_ egr}{Pb} \cdot \chi}\;{vex}\begin{matrix}{{{{\,\chi}\;{vex}} = \frac{14}{M + \alpha + \beta}}{{\chi\;{vegr}} = {{\chi\;{vb}} - {\chi\;{va}}}}} & \;\end{matrix}}} & (19)\end{matrix}$

From the derivation result of the equation (15), (P_egr/Pb) in theequation (19) is equal to the EGR rate Regr; thus, when the equation(15) is substituted for the equation (19) and then the equation (19) isrearranged, the equation (20) is obtained. Accordingly, the EGR rateRegr becomes a value obtained by dividing the mole fraction χvegr ofcombustion-produced water vapor in the intake manifold 12, calculated bysubtracting the mole fraction χva of the water vapor in the intake airfrom the mole fraction χvb of the water vapor in the intake manifold 12,by the mole fraction χvex of inner-exhaust-gas combustion-produced watervapor. In other words, it is suggested that by dividing the molefraction χvegr of combustion-produced water vapor in the intake manifold12 by the mole fraction χvex of inner-exhaust-gas combustion-producedwater vapor, the total mole fraction of all the recirculation exhaustgas in the gas inside the intake manifold 12 is obtained and that themole fraction of the recirculation exhaust gas is equal to the ratio(P_egr/Pb) of the partial pressure P_egr of the recirculation exhaustgas to the manifold pressure Pb, i.e., the recirculation exhaust gas.

$\begin{matrix}{{{Regr} = {\left( {{\chi\;{vb}} - {\chi\;{va}}} \right) \cdot \frac{1}{\chi\;{vex}}}}{{\chi\;{vex}} = \frac{14}{M + \alpha + \beta}}{{\chi\;{vegr}} = {{\chi\;{vb}} - {\chi\;{va}}}}} & (20)\end{matrix}$

By rearranging the equation (17) with respect to β, the number β ofmoles of water vapor in the intake air can be expressed by the equation(21).

$\begin{matrix}{\beta = {\frac{\chi\;{va}}{1 - {\chi\;{va}}} \cdot \left( {M + \alpha} \right)}} & (21)\end{matrix}$

By substituting the equation (21) for the equation (20) and thenrearranging the equation (20), the equation (22) is obtained. In theequation (22), the number α of moles of CO2 in the intake air is set to0.038, which is a nominal value.

$\begin{matrix}{\mspace{79mu}{{{Regr} = {\left( {{\chi\;{vb}} - {\chi\;{va}}} \right) \cdot \frac{1}{\chi\;{vex}}}}{{\chi\;{vex}} = {{\frac{14}{M + \alpha + {\frac{\chi\;{va}}{1 - {\chi\;{va}}} \cdot \left( {M + \alpha} \right)}} \cdot \left( {1 - {\chi\;{va}}} \right)} = {{\frac{14}{M + \alpha} \cdot \left( {1 - {\chi\;{va}}} \right)} = {\frac{14}{107 + 0.038} \cdot \left( {1 - {\chi\;{va}}} \right)}}}}}} & (22)\end{matrix}$

Thus, it is conceivable that from the derivation result of the equation(22), the EGR rate Regr can be calculated based on the mole fraction χvbof water vapor in the intake manifold 12 and the mole fraction χva ofwater vapor in intake air.

As represented in the equation (23), the mole fraction χvb of watervapor in the intake manifold 12 becomes theoretically equal to the ratio(Pvb/Pb) of the partial pressure Pvb of inner-manifold water vapor,which is the partial pressure of water vapor included in the gas insidethe intake manifold 12, to the manifold pressure Pb. The mole fractionχva of water vapor in the intake air becomes theoretically equal to theratio (Pva/Pa) of the partial pressure Pva of inner-intake-air watervapor, which is the partial pressure of water vapor included in theintake air, to the intake-air pressure Pa.

$\begin{matrix}{{{\chi\;{vb}} = \frac{Pvb}{Pb}}{{\chi\;{va}} = \frac{Pva}{Pa}}} & (23)\end{matrix}$

Thus, it is conceivable that as represented in the equation (24)obtained by substituting the equation (23) for the equation (22), theEGR rate Regr can be calculated by detecting the inner-manifold watervapor partial pressure ratio (Pvb/Pb), which is the ratio of the partialpressure Pvb of the inner-manifold water vapor to the manifold pressurePb, and the inner-intake-air water vapor partial pressure ratio(Pva/Pa), which is the ratio of the partial pressure Pva of theinner-intake-air water vapor to the intake-air pressure Pa.

$\begin{matrix}{{Regr} = {\left( {\frac{Pvb}{Pb} - \frac{Pva}{Pa}} \right) \cdot \frac{M + \alpha}{14} \cdot \frac{1}{1 - \frac{Pva}{Pa}}}} & (24)\end{matrix}$1-2-1-2. Configuration of the Humidity Detecting EGR Rate CalculationUnit 52

The humidity detecting EGR rate calculation unit 52 calculates thehumidity detecting EGR rate Regr based on the intake-air temperature Ta,the intake-air humidity Hra, the intake-air pressure Pa, the manifoldtemperature Tb, the manifold humidity Hrb, and the manifold pressure Pb.In Embodiment 1, the humidity detecting EGR rate calculation unit 52 isprovided with an inner-manifold water vapor ratio calculation unit 70,an inner-intake-air water vapor ratio calculation unit 71, and a finalEGR rate calculation unit 72, as shown in FIG. 2.

Based on the manifold humidity Hrb and the manifold temperature Tb whichare detected by the driving-condition detection unit 51, theinner-manifold water vapor ratio calculation unit 70 calculates thepartial pressure Pvb of the inner-manifold water vapor which is thepartial pressure of water vapor included in the gas inside the intakemanifold 12, so as to calculate the inner-manifold water vapor partialpressure ratio (Pvb/Pb) which is the ratio of the partial pressure Pvbof the inner-manifold water vapor to the manifold pressure Pb. Based onthe intake-air humidity Hra and the intake-air temperature Ta which aredetected by the driving-condition detection unit 51, theinner-intake-air water vapor ratio calculation unit 71 calculates thepartial pressure Pva of inner-intake-air water vapor, which is thepartial pressure of water vapor included in the intake air, so as tocalculate the inner-intake-air water vapor partial pressure ratio(Pva/Pa), which is the ratio of the partial pressure Pva of theinner-intake-air water vapor to the intake-air pressure Pa.

Then, based on the inner-manifold water vapor partial pressure ratio(Pvb/Pb) and the inner-intake-air water vapor partial pressure ratio(Pva/Pa), the final EGR rate calculation unit 72 calculates the humiditydetecting EGR rate Regr, which is the ratio of recirculation exhaustgas, recirculated into the intake manifold 12, to the gas in the intakemanifold 12.

This configuration makes it possible that based on the detection valuesof the pressure, the temperature, and the humidity of each of gas andintake air in the intake manifold 12, the inner-manifold water vaporpartial pressure ratio (Pvb/Pb) and the inner-intake-air water vaporpartial pressure ratio (Pva/Pa) are calculated and that based on thesetwo water vapor partial pressure ratios, the humidity detecting EGR rateRegr is accurately calculated. The details will be explained below.

<The Inner-Manifold Water Vapor Ratio Calculation Unit 70>

As described above, based on the manifold humidity Hrb and the manifoldtemperature Tb, the inner-manifold water vapor ratio calculation unit 70calculates the partial pressure Pvb of the inner-manifold water vapor,which is the partial pressure of water vapor included in the gas insidethe intake manifold 12, so as to calculate the inner-manifold watervapor partial pressure ratio (Pvb/Pb), which is the ratio of the partialpressure Pvb of the inner-manifold water vapor to the manifold pressurePb.

As described above, the inner-manifold water vapor partial pressureratio (Pvb/Pb) is theoretically equal to the water vapor mole fractionχvb, which is the ratio of the number of moles of water vapor to thenumber of total moles of gas in the intake manifold 12. Therefore, theinner-manifold water vapor partial pressure ratio (Pvb/Pb) can bereferred to also as the water vapor mole fraction χvb.

In Embodiment 1, the inner-manifold water vapor ratio calculation unit70 calculates a saturated water vapor pressure Psb in the intakemanifold 12, based on the manifold temperature Tb, and then calculatesthe partial pressure Pvb of the inner-manifold water vapor bymultiplying the saturated water vapor pressure Psb by the manifoldhumidity Hrb, which is a relative humidity.

Specifically, the inner-manifold water vapor ratio calculation unit 70calculates the saturated water vapor pressure Psb in the intake manifold12 by use of the Tetens equation represented in the equation (25).

$\begin{matrix}{{Psb} = {6.1078 \times 10^{(\frac{7.5 \times {Tb}}{{Tb} + 237.3})}}} & (25)\end{matrix}$

The inner-manifold water vapor ratio calculation unit 70 may calculatethe saturated water vapor pressure Psb corresponding to the manifoldtemperature Tb, by use of a characteristic data in which therelationship between the temperature and the saturated water vaporpressure is preliminarily set based on the equation (25).

Then, as represented in the equation (26), the inner-manifold watervapor ratio calculation unit 70 calculates the partial pressure Pvb ofthe inner-manifold water vapor, by multiplying the saturated water vaporpressure Psb by the manifold humidity Hrb [% RH], and then calculatesthe inner-manifold water vapor partial pressure ratio (Pvb/Pb), bydividing the partial pressure Pvb of the inner-manifold water vapor bythe manifold pressure Pb.

$\begin{matrix}{{Pvb} = {{Psb} \cdot \frac{Hrb}{100}}} & (26)\end{matrix}$<The Inner-Intake-Air Water Vapor Ratio Calculation Unit 71>

As described above, based on the intake-air humidity Hra and theintake-air temperature Ta, the inner-intake-air water vapor ratiocalculation unit 71 calculates the partial pressure Pva ofinner-intake-air water vapor, which is the partial pressure of watervapor included in the intake air, so as to calculate theinner-intake-air water vapor partial pressure ratio (Pva/Pa), which isthe ratio of the partial pressure Pva of the inner-intake-air watervapor to the intake-air pressure Pa.

As described above, the inner-intake-air water vapor partial pressureratio (Pva/Pa) is theoretically equal to the water vapor mole fractionχva, which is the ratio of the number of moles of water vapor to thenumber of total moles of intake air. Thus, the inner-intake-air watervapor partial pressure ratio (Pva/Pa) can be referred to also as theinner-intake-air water vapor mole fraction χva.

In Embodiment 1, based on the intake-air temperature Ta, theinner-intake-air water vapor ratio calculation unit 71 calculates asaturated water vapor pressure Psa of intake air and then calculates theinner-intake-air water vapor partial pressure Pva by multiplying thesaturated water vapor pressure Psa by the intake-air humidity Hra, whichis a relative humidity.

Specifically, the inner-intake-air water vapor ratio calculation unit 71calculates the saturated water vapor pressure Psa of the intake air byuse of the Tetens equation represented in the equation (27).

$\begin{matrix}{{Psa} = {6.1078 \times 10^{(\frac{7.5 \times {Ta}}{{Ta} + 237.3})}}} & (27)\end{matrix}$

The inner-intake-air water vapor ratio calculation unit 71 may calculatethe saturated water vapor pressure Psa corresponding to the intake-airtemperature Ta by use of a characteristic data in which the relationshipbetween the temperature and the saturated water vapor pressure ispreliminarily set.

Then, as represented in the equation (28), the inner-intake-air watervapor ratio calculation unit 71 calculates the inner-intake-air watervapor partial pressure Pva by multiplying the saturated water vaporpressure Psa by the intake-air humidity Hra [% RH], and then calculatesthe inner-intake-air water vapor partial pressure ratio (Pva/Pa), bydividing the partial pressure Pva of the inner-intake-air water vapor bythe intake-air pressure Pa.

$\begin{matrix}{{Pva} = {{Psa} \cdot \frac{Hra}{100}}} & (28)\end{matrix}$<The Final EGR Rate Calculation Unit 72>

As described above, based on the inner-manifold water vapor partialpressure ratio (Pvb/Pb) and the inner-intake-air water vapor partialpressure ratio (Pva/Pa), the final EGR rate calculation unit 72calculates the humidity detecting EGR rate Regr, which is the ratio ofrecirculation exhaust gas, recirculated into the intake manifold 12, tothe gas in the intake manifold 12.

The final EGR rate calculation unit 72 calculates the humidity detectingEGR rate Regr by use of the equation (29) based on the equation (24)above. In other words, the final EGR rate calculation unit 72 calculatesa subtraction partial pressure ratio by subtracting the inner-intake-airwater vapor partial pressure ratio (Pva/Pa) from the inner-manifoldwater vapor partial pressure ratio (Pvb/Pb), multiplies the subtractionpartial pressure ratio by a preliminarily set conversion constant Kr,then calculates, as the humidity detecting EGR rate Regr, a value bydividing the multiplication value by a subtraction value obtained bysubtracting the inner-intake-air water vapor partial pressure ratio(Pva/Pa) from “1”.

$\begin{matrix}{{{Regr} = {\left( {\frac{Pvb}{Pb} - \frac{Pva}{Pa}} \right) \cdot {Kr} \cdot \frac{1}{1 - \frac{Pva}{Pa}}}}{{Kr} = {\frac{M + \alpha}{14} = \frac{107 + 0.038}{14}}}} & (29)\end{matrix}$

Based on the respective numbers of moles of molecules in the chemicalreaction formula at a time when a fuel and wet air combust together, theconversion constant Kr is preliminarily set as represented in theequation (29). Specifically, the conversion constant Kr is preliminarilyset to a fixed value obtained by dividing a value (107+0.038, in thisexample), calculated by subtracting the number β of moles ofinner-intake-air water vapor from the number (M+α+β) of total moles ofexhaust gas in the right-hand side (combusted gas) of the combustionchemical reaction formula represented in the equation (14), by thenumber of moles of the combustion-produced water vapor (14, in thisexample). The conversion constant Kr may be a value other than the valuerepresented in the equation (29), for example, a value obtained throughadjustment based on an experimental value. Because sufficiently smallerthan M, the number α of moles of inner-intake-air carbon dioxide may beregarded as zero.

The calculation by the equation (29) will be expressed based on physicalquantities. The equation (30) is obtained by modifying the equation(29). As represented in the equation (30), the final EGR ratecalculation unit 72 calculates an inner-manifold combustion-producedwater vapor partial pressure ratio (Pvegr/Pb), which is the ratio of thepartial pressure Pvegr (referred to as an inner-intake-manifoldcombustion-produced water vapor partial pressure Pvegr) ofcombustion-produced water vapor included in recirculation exhaust gas tothe manifold pressure Pb, by subtracting the inner-intake-air watervapor partial pressure ratio (Pva/Pa) from the inner-manifold watervapor partial pressure ratio (Pvb/Pb). Based on the number of moles ofmolecules in the chemical reaction formula at a time when a fuel and wetair combust together and the inner-intake-air water vapor partialpressure ratio (Pva/Pa), the final EGR rate calculation unit 72calculates the inner-exhaust-gas combustion-produced water vapor molefraction χvex, which is the mole fraction of combustion-produced watervapor in exhaust gas. Then, the final EGR rate calculation unit 72calculates, as the humidity detecting EGR rate Regr, a value by dividingthe inner-manifold combustion-produced water vapor partial pressureratio (Pvegr/Pb) by the inner-exhaust-gas combustion-produced watervapor mole fraction χvex.

$\begin{matrix}{{{Regr} = {\frac{Pvegr}{Pb} \cdot \frac{1}{\chi\;{vex}}}}{\frac{Pvegr}{Pb} = {\frac{Pvb}{Pb} - \frac{Pva}{Pa}}}{{\chi\;{vex}} = {{Kr}\;{2 \cdot \left( {1 - \frac{Pva}{Pa}} \right)}}}{{{Kr}\; 2} = {\frac{14}{M + \alpha} = \frac{14}{107 + 0.038}}}} & (30)\end{matrix}$

Speaking in detail, the final EGR rate calculation unit 72 calculates,as the inner-exhaust-gas combustion-produced water vapor mole fractionχvex, a value by multiplying a preliminarily set mole conversionconstant Kr2 by a subtraction value calculated by subtracting theinner-intake-air water vapor partial pressure ratio (Pva/Pa) from “1”.As is the case with the foregoing conversion constant Kr, the moleconversion constant Kr2 is preliminarily set based on an experimentalvalue, the respective numbers of moles of molecules in the chemicalreaction formula at a time when a fuel and wet air combust together, orthe like. The calculation equation for the inner-exhaust-gascombustion-produced water vapor mole fraction χvex is derived bysubstituting the equation (21), derived based on the combustion chemicalreaction formula represented in the equation (14), for the equation(20), derived based on the combustion chemical reaction formularepresented in the equation (14).

As described above, by dividing the inner-manifold combustion-producedwater vapor partial pressure ratio (Pvegr/Pb) by the inner-exhaust-gascombustion-produced water vapor mole fraction χvex, the ratio (P_egr/Pb)of the partial pressure P_egr of recirculation exhaust gas to themanifold pressure Pb is obtained and hence the humidity detecting EGRrate Regr is obtained.

1-2-2. Flowchart

The procedure (the control method for the internal combustion engine 1)of the processing by the controller 50 according to Embodiment 1 will beexplained based on the flowchart represented in FIG. 5. The processingrepresented in the flowchart in FIG. 5 is recurrently implemented, forexample, every constant operation cycle while the computing processingunit 90 implements software (a program) stored in the storage apparatus91.

In the step S01, the driving-condition detection unit 51 implementsdriving condition detection processing (a driving condition detectionstep) for, as mentioned above, detecting the driving condition of theinternal combustion engine 1. The driving-condition detection unit 51detects the manifold pressure Pb, the manifold temperature Tb, themanifold humidity Hrb, the intake-air pressure Pa, the intake-airtemperature Ta, the intake-air humidity Hra, the intake air flow rateQa, the opening degree Oe of the EGR valve 22, and the like.

Next, in the step S02, the humidity detecting EGR rate calculation unit52 implements a humidity detecting EGR rate calculation processing (ahumidity detecting EGR rate calculation Step) for, as mentioned above,calculating the humidity detecting EGR rate Regr based on the intake-airtemperature Ta, the intake-air humidity Hra, the intake-air pressure Pa,the manifold temperature Tb, the manifold humidity Hrb, and the manifoldpressure Pb. In the step S02, an inner-manifold water vapor ratiocalculation processing (an inner-manifold water vapor ratio calculationstep) performed by the inner-manifold water vapor ratio calculation unit70, an inner-intake-air water vapor ratio calculation processing (aninner-intake-air water vapor ratio calculation step) performed by theinner-intake-air water vapor ratio calculation unit 71, and a final EGRrate calculation processing (a final EGR rate calculation Step)performed by the final EGR rate calculation unit 72 are performed inorder.

In the step S03, the opening area learning value calculation unit 53implements an opening area learning value calculation processing (anopening area learning value calculation step) for, as mentioned above,calculating the humidity detecting recirculation flow rate Qeh based onthe humidity detecting EGR rate Regr and the intake air flow rate Qa,calculating the humidity detecting opening area Segrh, which is anopening area of the EGR valve 22 which realizes the humidity detectingrecirculation flow rate Qeh, and calculating the learning value ΔSegrLof the opening area of the EGR valve 22 based on the humidity detectingopening area Segrh.

In the step S04, the recirculation exhaust gas calculation unit forcontrol 54 implements a recirculation exhaust gas calculation processingfor control (a recirculation exhaust gas calculation step for control)for, as mentioned above, calculating the learned opening area SegrL ofthe EGR valve 22 corresponding to the present opening degree Oe of theEGR valve 22 using the learning value ΔSegrL of opening area, andcalculating the flow rate Qes of the recirculation exhaust gas forcontrol used for control of the internal combustion engine 1 based onthe learned opening area SegrL.

In the step S05, the recirculation amount utilization control unit 55implements a recirculation amount utilization control processing (arecirculation amount utilization control step) for, as mentioned above,controlling the internal combustion engine 1 using the recirculationexhaust gas flow rate Qes for control.

2. Embodiment 2

Next, the controller 50 according to Embodiment 2 will be explained. Theexplanation for constituent parts the same as those in Embodiment 1 willbe omitted. The respective basic configurations and processing methodsof the internal combustion engine 1 and the controller 50 according toEmbodiment 2 are the same as those of the internal combustion engine 1and the controller 50 according to Embodiment 1; however, Embodiment 2is different from Embodiment 1 in that the humidity detecting EGR ratecalculation unit 52 changes the humidity detecting EGR rate Regr inaccordance with the air-fuel ratio AF of the internal combustion engine1.

2-1. Extension of the Calculation Method for the Humidity Detecting EGRRate Regr to the Case of Rich- or Lean-Air-Fuel Ratio

The calculation method for the humidity detecting EGR rate Regraccording to Embodiment 1 is based on the combustion chemical reactionformula represented in the equation (14) at a time when a fuel and wetair combust together at the theoretical air-fuel ratio AF0. Hereinafter,the equation derivation will be extended to the case where the air-fuelratio of wet air to a fuel is leaner than the theoretical air-fuel ratioAF0 or to the case where the air-fuel ratio is richer that thetheoretical air-fuel ratio AF0.

An excess air ratio λ is the ratio of the air-fuel ratio AF to thetheoretical air-fuel ratio AF0, as represented in the equation (31).When λ=1, the air-fuel ratio AF is equal to the theoretical air-fuelratio AF0; when λ<1, the air-fuel ratio AF is rich; when λ>1, theair-fuel ratio AF is lean.

$\begin{matrix}{\lambda = \frac{AF}{{AF}\; 0}} & (31)\end{matrix}$<In the Case of Rich Air-Fuel Ratio>

The equation (32) represents the combustion chemical reaction formula ata time when the air-fuel ratio AF is rich (λ<1).2.C₇H₁₄+λ·{21.O₂+79.N₂+α.CO₂+β.H₂O}→λ·{(14+α).CO₂+(14+β).H₂O+79.N₂}+(1−λ).2.C₇H₁₄  (32)

In this situation, as represented by the last term in the right-handside of the equation (32), it is assumed that in the case of richcombustion, uncombusted gasoline is directly exhausted with its originalmolecules. In practice, it is conceivable that due to the combustiontemperature in the cylinder 25, uncombusted gasoline is decomposed intomethane (CH4), ethane (C2H6), and the like that each have a molecularweight smaller than that of gasoline; however, because the volumeconcentration of gasoline is small and the decomposition of gasoline maynot provide a substantial effect, the decomposition of gasoline is nottaken into consideration in this embodiment.

As represented in the equation (33), the concentration CO2_ex of CO2 inexhaust gas is equal to the ratio (the mole fraction of CO2) of thenumber of moles of CO2 to the number of total moles in the exhaust gasrepresented in the right-hand side of the equation (32). Because beingsmall in comparison with the number of total moles, the number ((1−λ)·2)of moles of uncombusted gasoline is approximated with zero. Similarly,the concentration CO2_in of CO2 in the gas inside the intake manifold 12and the concentration CO2_a of CO2 in the intake air are also obtained.From the equation (33), the concentration of CO2 at a time when theair-fuel ratio is rich becomes equal to the concentration of CO2represented in the equation (15) at a time of the theoretical air-fuelratio AF0. Therefore, in the case where the air-fuel ratio is rich, theEGR rate Regr becomes the ratio (P_egr/Pb) of the partial pressure P_egrof the recirculation exhaust gas to the manifold pressure Pb, as is thecase with the equation (16).

$\begin{matrix}{\begin{matrix}{{CO}_{2{\_ ex}} = \frac{\lambda \cdot \left( {14 + \alpha} \right)}{{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}} + {\left( {1 - \lambda} \right) \cdot 2}}} \\{\cong \frac{\lambda \cdot \left( {14 + \alpha} \right)}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} \\{= \frac{14 + \alpha}{M + \alpha + \beta}}\end{matrix}\begin{matrix}{{CO}_{2{\_{in}}} = {{\frac{P\_ new}{Pb} \cdot \frac{\lambda \cdot \alpha}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} + {\frac{P\_ egr}{Pb} \cdot}}} \\{\frac{\lambda \cdot \left( {14 + \alpha} \right)}{{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}} + {\left( {1 - \lambda} \right) \cdot 2}}} \\{\cong {{\frac{P\_ new}{Pb} \cdot \frac{\alpha}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot \frac{14 + \alpha}{M + \alpha + \beta}}}}\end{matrix}{{\begin{matrix}{{CO}_{2{\_ a}} = \frac{\lambda \cdot \alpha}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} \\{= \frac{\alpha}{M + \alpha + \beta}}\end{matrix}\therefore{Regr}} = \frac{P\_ egr}{Pb}}} & (33)\end{matrix}$

In the case where the air-fuel ratio is rich, the mole fraction χva ofwater vapor in the intake air and the mole fraction χvb of water vaporin the gas in the intake manifold 12 are represented by the equation(34) by use of the mole fraction of water vapor in the left-hand side orthe right-hand side of the equation (32) and the like, as is the casewith the respective mole fractions at a time of the theoretical air-fuelratio AF0 represented in the equations (17) and (18).

$\begin{matrix}{\begin{matrix}{{\chi\;{va}} = \frac{\lambda \cdot \beta}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} \\{= \frac{\beta}{M + \alpha + \beta}}\end{matrix}\begin{matrix}{{\chi\;{vb}} = {{\frac{P\_ new}{Pb} \cdot \frac{\lambda \cdot \beta}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} + {\frac{P\_ egr}{Pb} \cdot}}} \\{\frac{\lambda \cdot \left( {14 + \beta} \right)}{{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}} + {\left( {1 - \lambda} \right) \cdot 2}}} \\{\cong {{\frac{P\_ new}{Pb} \cdot \frac{\beta}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot \frac{14 + \beta}{M + \alpha + \beta}}}} \\{= {\frac{\beta}{M + \alpha + \beta} + {\frac{P\_ egr}{Pb} \cdot \frac{14}{M + \alpha + \beta}}}}\end{matrix}} & (34)\end{matrix}$

From the equation (34), the mole fractions χva and χvb of water vapor ata time when the air-fuel ratio is rich become equal to those representedin the equations (17) and (18), respectively, at a time of thetheoretical air-fuel ratio AF0. When at a time of a rich air-fuel ratio(λ<1), uncombusted gasoline is produced and hence the numerator, i.e.,the number of moles of combustion-produced water vapor is obtained bymultiplying the number of moles of combustion-produced water vapor at atime of the theoretical air-fuel ratio AF0, i.e., 14 by λ; however,because the respective numbers of moles of the molecules in the intakeair are multiplied by λ, the denominator, i.e., the number of totalmoles of exhaust gas is also obtained by multiplying the number of totalmoles of exhaust gas at a time of the theoretical air-fuel ratio AF0 byλ. As a result, λ in the numerator and λ in the denominator cancel eachother and hence the respective values the same as those at a time of thetheoretical air-fuel ratio AF0 can be obtained. Accordingly, when theair fuel ratio is rich, the EGR rate Regr can be calculated by theequation (34), which is the equation for the case where the air fuelratio is the theoretical air-fuel ratio AF0.

<In the Case of Lean Air-Fuel Ratio>

The equation (35) represents the combustion chemical reaction formula ata time when the air-fuel ratio AF is lean (λ>1).2.C₇H₁₄+λ.{21.O₂+79.N₂+α.CO₂+β.H₂O}→(14+λ·α).CO₂+(14+λ·β).H₂O+λ·79.N₂+21·(λ−1).O₂  (35)

As represented in the equation (36), the concentration CO2_ex of CO2 inexhaust gas is equal to the ratio (the mole fraction of CO2) of thenumber of moles of CO2 to the number of total moles in the exhaust gasrepresented in the right-hand side of the equation (35). Because beingsmall in comparison with the number of total moles, the number of moles“7” is approximated with zero. Similarly, the concentration CO2_in ofCO2 in the gas inside the intake manifold 12 and the concentration CO2_aof CO2 in the intake air are also obtained. From the equation (36), theconcentration of CO2 at a time when the air-fuel ratio is lean differsfrom the concentration of CO2 represented in the equation (15) at a timeof the theoretical air-fuel ratio AF0.

$\begin{matrix}{\begin{matrix}{{CO}_{2{\_ ex}} = \frac{\left( {14 + {\lambda \cdot \alpha}} \right)}{\left( {14 + {\lambda \cdot \alpha}} \right) + \left( {14 + {\lambda \cdot \beta}} \right) + {\lambda \cdot 79} + {21 \cdot \left( {\lambda - 1} \right)}}} \\{= \frac{14 + {\lambda \cdot \alpha}}{{\lambda \cdot \left( {M + \alpha + \beta} \right)} + 7}} \\{\cong \frac{14 + {\lambda \cdot \alpha}}{\lambda \cdot \left( {M + \alpha + \beta} \right)}}\end{matrix}\begin{matrix}{{CO}_{2{\_{in}}} = {{\frac{P\_ new}{Pb} \cdot \frac{\lambda \cdot \alpha}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} + {\frac{P\_ egr}{Pb} \cdot}}} \\{\frac{14 + {\lambda \cdot \alpha}}{{\lambda \cdot \left( {M + \alpha + \beta} \right)} + 7}} \\{\cong {{\frac{P\_ new}{Pb} \cdot \frac{\alpha}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot \frac{14 + {\lambda \cdot \alpha}}{\lambda \cdot \left( {M + \alpha + \beta} \right)}}}}\end{matrix}\begin{matrix}{{CO}_{2{\_ a}} = \frac{\lambda \cdot \alpha}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} \\{= \frac{\alpha}{M + \alpha + \beta}}\end{matrix}} & (36)\end{matrix}$

Then, by substituting the respective concentrations of CO2 in theequation (36) for the equation (11) and then rearranging the equation(1), the equation (37) is obtained. In the case where the air-fuel ratiois lean, the EGR rate Regr also becomes the ratio (P_egr/Pb) of thepartial pressure P_egr of the recirculation exhaust gas to the manifoldpressure Pb, as is the case with the equation (16).

$\begin{matrix}\begin{matrix}{{Regr} = \frac{{CO}_{2{\_ in}} - {CO}_{2{\_ a}}}{{CO}_{2{\_ ex}} - {CO}_{2{\_ a}}}} \\{= \frac{\begin{matrix}{\left( {{\frac{P\_ new}{Pb} \cdot \frac{\alpha}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot \frac{14 + {\lambda \cdot \alpha}}{\lambda \cdot \left( {M + \alpha + \beta} \right)}}} \right) -} \\\left( \frac{\alpha}{M + \alpha + \beta} \right)\end{matrix}}{\left( \frac{14 + {\lambda\_\alpha}}{\lambda \cdot \left( {M + \alpha + \beta} \right)} \right) - \left( \frac{\alpha}{M + \alpha + \beta} \right)}} \\{= \frac{P\_ egr}{Pb}}\end{matrix} & (37)\end{matrix}$

In the case where the air-fuel ratio is lean, the mole fraction χva ofwater vapor in the intake air and the mole fraction χvb of water vaporin the gas in the intake manifold 12 are represented by the equation(38) by use of the mole fraction of water vapor in the left-hand side orthe right-hand side of the equation (35) and the like, as is the casewith the respective mole fractions at a time of the theoretical air-fuelratio AF0 represented in the equations (17) and (18).

$\begin{matrix}{\begin{matrix}{{\chi\;{va}} = \frac{\lambda \cdot \beta}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} \\{= \frac{\beta}{M + \alpha + \beta}}\end{matrix}\begin{matrix}{{\chi\;{vb}} = {{\frac{P\_ new}{Pb} \cdot \frac{\lambda \cdot \beta}{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}}} + {\frac{P\_ egr}{Pb} \cdot}}} \\{\frac{14 + {\lambda \cdot \beta}}{{\lambda \cdot \left\{ {M + \alpha + \beta} \right\}} + 7}} \\{\cong {{\frac{P\_ new}{Pb} \cdot \frac{\beta}{M + \alpha + \beta}} + {\frac{P\_ egr}{Pb} \cdot \frac{14 + {\lambda \cdot \beta}}{\lambda \cdot \left( {M + \alpha + \beta} \right)}}}} \\{= {\frac{\beta}{M + \alpha + \beta} + {\frac{P\_ egr}{Pb} \cdot \frac{14}{\lambda \cdot \left( {M + \alpha + \beta} \right)}}}}\end{matrix}} & (38)\end{matrix}$

By rearranging the equation (38), as is the case with the equation (19),the equation (39) is obtained. The inner-exhaust-gas combustion-producedwater vapor mole fraction χvexL at a time when the air-fuel ratio islean becomes a value obtained by dividing the inner-exhaust-gascombustion-produced water vapor mole fraction χvex, represented in theequation (19), at a time of the theoretical air-fuel ratio AF0 by theexcess air ratio λ. The reason for that is the following: when at a timeof a lean air-fuel ratio (λ>1), the fuel completely combusts and hencethe numerator, i.e., the number of moles of combustion-produced watervapor is the same as the number of moles of combustion-produced watervapor at a time of the theoretical air-fuel ratio AF0, i.e., 14; incontrast, because the respective numbers of moles of the molecules inthe intake air are multiplied by λ, the denominator, i.e., the number oftotal moles of exhaust gas is obtained by multiplying the number oftotal moles of exhaust gas at a time of the theoretical air-fuel ratioAF0 by λ.

$\begin{matrix}{{{{\chi\;{vb}} - {\chi\;{va}}} = {{\frac{P\_ egr}{Pb} \cdot \chi}\;{vexL}}}{{\chi\;{vexL}} = {\frac{1}{\lambda} \cdot \frac{14}{M + \alpha + \beta}}}{{\chi\;{vegr}} = {{\chi\;{vb}} - {\chi\;{va}}}}} & (39)\end{matrix}$

By substituting the equation (37) for the equation (39) and thenrearranging the equation (39), the equation (40) is obtained.

$\begin{matrix}{{{Regr} = {\left( {{\chi\;{vb}} - {\chi\;{va}}} \right) \cdot \frac{1}{\chi\;{vexL}}}}{{\chi\;{vexL}} = {{{\frac{1}{\lambda} \cdot \frac{14}{M + \alpha + \beta}}\chi\;{vegr}} = {{\chi\;{vb}} - {\chi\;{va}}}}}} & (40)\end{matrix}$

The number β of moles of water vapor in the intake air is given by theequation (21), as is the case with the theoretical air-fuel ratio AF0;thus, by substituting the equation (21) for the equation (40) andrearranging the equation (40), the equation (41) is obtained.

$\begin{matrix}{{{Regr} = {\left( {{\chi\;{vb}} - {\chi\;{va}}} \right) \cdot \frac{1}{\chi\;{vexL}}}}\begin{matrix}{{\chi\;{vexL}} = {\frac{1}{\lambda} \cdot \frac{14}{M + \alpha + {\frac{\chi\;{va}}{1 - {\chi\;{va}}} \cdot \left( {M + \alpha} \right)}} \cdot \left( {1 - {\chi\;{va}}} \right)}} \\{= {\frac{1}{\lambda} \cdot \frac{14}{M + \alpha} \cdot \left( {1 - {\chi\;{va}}} \right)}}\end{matrix}} & (41)\end{matrix}$

Then, by substituting the equation (23) for the equation (41) and thenrearranging the equation (41), the equation (42) is obtained. Therefore,in the case of a lean air-fuel ratio, the EGR rate Regr can becalculated by multiplying the EGR rate Regr, represented in the equation(24), at a time of the theoretical air-fuel ratio AF0 by the excess airratio λ.

$\begin{matrix}{{Regr} = {\lambda \cdot \left( {\frac{Pvb}{Pb} - \frac{Pva}{Pa}} \right) \cdot \frac{M + \alpha}{14} \cdot \frac{1}{1 - \frac{Pva}{Pa}}}} & (42)\end{matrix}$

The foregoing derivation results will be summarized in the equation(43). In the case where the air-fuel ratio AF of the internal combustionengine 1 is the theoretical air-fuel ratio (AF=AF0) or rich (AF<AF0),the EGR rate Regr can be calculated, through the equation (24), based onthe inner-manifold water vapor partial pressure ratio (Pvb/Pb) and theinner-intake-air water vapor partial pressure ratio (Pva/Pa). In thecase where the air-fuel ratio AF of the internal combustion engine 1 islean (AF>AF0), the EGR rate Regr can be calculated by, as represented inthe equation (42), further multiplying the EGR rate Regr calculatedthrough the equation (24) by the excess air ratio λ.

$\begin{matrix}{\left. 1 \right)\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{case}\mspace{14mu}{of}\mspace{14mu}{theoretical}\mspace{14mu}{air}\text{/}{fuel}\mspace{14mu}{ratio}\mspace{14mu}{or}\mspace{14mu}{rich}} & \; \\{{\left. {{{Regr} = {\left( {\frac{Pvb}{Pb} - \frac{Pva}{Pa}} \right) \cdot \frac{M + \alpha}{14} \cdot \frac{1}{1 - \frac{Pva}{Pa}}}}2} \right)\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{case}\mspace{14mu}{of}\mspace{14mu}{lean}}{{Regr} = {\lambda \cdot \left( {\frac{Pvb}{Pb} - \frac{Pva}{Pa}} \right) \cdot \frac{M + \alpha}{14} \cdot \frac{1}{1 - \frac{Pva}{Pa}}}}} & (43)\end{matrix}$2-2. The Configuration of the Final EGR Rate Calculation Unit 72

Thus, the final EGR rate calculation unit 72 according to Embodiment 2changes the humidity detecting EGR rate Regr in accordance with theair-fuel ratio AF of the internal combustion engine 1.

As is the case with the equation (29) or (30) in Embodiment 1, the finalEGR rate calculation unit 72 calculates the humidity detecting EGR rateRegr0 at a time when it is assumed that the air-fuel ratio AF of theinternal combustion engine 1 is the theoretical air-fuel ratio, based onthe inner-manifold water vapor partial pressure ratio (Pvb/Pb) and theinner-intake-air water vapor partial pressure ratio (Pva/Pa). Asrepresented in the equation (44), in the case where the air-fuel ratioAF is leaner than the theoretical air-fuel ratio AF0, the final EGR ratecalculation unit 72 calculates, as the final humidity detecting EGR rateRegr, a value by multiplying the humidity detecting EGR rate Regr0 at atime when it is assumed that the air-fuel ratio is the theoreticalair-fuel ratio AF0 by the excess air ratio λ obtained by dividing theair-fuel ratio AF by the theoretical air-fuel ratio AF0. On the otherhand, in the case where the air-fuel ratio AF is richer than thetheoretical air-fuel ratio AF0, the final EGR rate calculation unit 72directly calculates, as the final humidity detecting EGR rate Regr, thehumidity detecting EGR rate Regr0 at a time when it is assumed that theair-fuel ratio is the theoretical air-fuel ratio AF0.

1) in the case of leanRegr=λ·Regr0λ=AF/AF0  (44)

2) in the case of theoretical air/fuel ratio or richRegr=Regr0

Expression will be made based on physical quantities. As represented inthe equation (45), the final EGR rate calculation unit 72 calculates, asis the case with the equation (40) in Embodiment 1, theinner-exhaust-gas combustion-produced water vapor mole fraction χvex0 ata time when it is assumed that the air-fuel ratio AF of the internalcombustion engine 1 is the theoretical air-fuel ratio, based on therespective numbers of moles of molecules in the chemical reactionformula at a time when the fuel and wet air combust together at thetheoretical air-fuel ratio AF0 and the inner-intake-air water vaporpartial pressure ratio (Pva/Pa). The final EGR rate calculation unit 72calculates the inner-manifold combustion-produced water vapor partialpressure ratio (Pvegr/Pb) by subtracting the inner-intake-air watervapor partial pressure ratio (Pva/Pa) from the inner-manifold watervapor partial pressure ratio (Pvb/Pb).

$\begin{matrix}{{{{\chi\;{vex}\; 0} = {{Kr}\;{2 \cdot \left( {1 - \frac{Pva}{Pa}} \right)}}},{{{Kr}\; 2} = {\frac{14}{M + \alpha} = \frac{14}{107 + 0.038}}}}{\frac{Pvegr}{Pb} = {\frac{Pvb}{Pb} - \frac{Pva}{Pa}}}} & (45)\end{matrix}$

As represented in the equation (46), in the case where the air-fuelratio AF is leaner than the theoretical air-fuel ratio AF0, the finalEGR rate calculation unit 72 calculates, as the inner-exhaust-gascombustion-produced water vapor mole fraction χvexL at a time of a leanair-fuel ratio, a value by dividing the inner-exhaust-gascombustion-produced water vapor mole fraction χvex0 at a time when it isassumed that the air-fuel ratio is the theoretical air-fuel ratio AF0 bythe excess air ratio λ. Then, the final EGR rate calculation unit 72calculates, as the humidity detecting EGR rate Regr, a value by dividingthe inner-manifold combustion-produced water vapor partial pressureratio (Pvegr/Pb) by the inner-exhaust-gas combustion-produced watervapor mole fraction χvexL at a time of a lean air-fuel ratio. On theother hand, in the case where the air-fuel ratio AF is richer than thetheoretical air-fuel ratio AF0, the final EGR rate calculation unit 72directly adopts, as the inner-exhaust-gas combustion-produced watervapor mole fraction χvex0 at a time of a rich air-fuel ratio, theinner-exhaust-gas combustion-produced water vapor mole fraction χvex0 ata time when it is assumed that the air-fuel ratio is the theoreticalair-fuel ratio AF0. Then, the final EGR rate calculation unit 72calculates, as the humidity detecting EGR rate Regr, a value by dividingthe inner-manifold combustion-produced water vapor partial pressureratio (Pvegr/Pb) by the inner-exhaust-gas combustion-produced watervapor mole fraction χvex0 at a time of a rich air-fuel ratio.

$\begin{matrix}{\left. 1 \right)\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{case}\mspace{14mu}{of}\mspace{14mu}{lean}} & \; \\{{\left. {{{\chi\;{vexL}} = {{\frac{1}{\lambda} \cdot \chi}\;{vex}\; 0}}{{Regr} = {\frac{Pvegr}{Pb} \cdot \frac{1}{\chi\;{vexL}}}}2} \right)\mspace{14mu}{in}\mspace{14mu}{the}\mspace{14mu}{case}\mspace{14mu}{of}\mspace{14mu}{theoretical}\mspace{14mu}{air}\text{/}{fuel}\mspace{14mu}{ratio}\mspace{14mu}{or}\mspace{14mu}{rich}}{{Regr} = {\frac{Pvegr}{Pb} \cdot \frac{1}{\chi\;{vex}\; 0}}}} & (46)\end{matrix}$

Based on the air-fuel ratio AF detected by the air-fuel ratio sensor 18,the final EGR rate calculation unit 72 determines whether the air-fuelratio AF is rich, lean, or the theoretical air-fuel ratio, andcalculates the excess air ratio λ. Specifically, in the case where thedetection value of the air-fuel ratio AF is smaller than a preliminarilyset value (e.g., 14.7) of the theoretical air-fuel ratio AF0 (AF<AF0),the final EGR rate calculation unit 72 determines that the air-fuelratio is rich; in the case where the detection value of the air-fuelratio AF is larger than the setting value of the theoretical air-fuelratio AF0 (AF>AF0), the final EGR rate calculation unit 72 determinesthat the air-fuel ratio is lean; in the case where the detection valueof the air-fuel ratio AF is equal to the setting value of thetheoretical air-fuel ratio AF0 (AF=AF0), the final EGR rate calculationunit 72 determines that the air-fuel ratio is the theoretical air-fuelratio. In addition, the final EGR rate calculation unit 72 calculatesthe excess air ratio λ (=AF/AF0) by dividing the detection value of theair-fuel ratio AF by the preliminarily set value of the theoreticalair-fuel ratio AF0.

Alternatively, it may be allowed that based on a fuel correctioncoefficient Kaf to be utilized in calculating the fuel injection amount,the final EGR rate calculation unit 72 determines whether the air-fuelratio AF is rich, lean, or the theoretical air-fuel ratio, andcalculates the excess air ratio λ. For example, the fuel correctioncoefficient Kaf is a correction coefficient by which a basic fuelinjection amount calculated so as to realize the theoretical air-fuelratio AF0 is multiplied. In the case where Kaf=1, the final EGR ratecalculation unit 72 determines that the air-fuel ratio is thetheoretical air-fuel ratio AF0; in the case where Kaf>1, the final EGRrate calculation unit 72 determines that the air-fuel ratio is rich; inthe case where Kaf<1, the final EGR rate calculation unit 72 determinesthat the air-fuel ratio is lean. As the excess air ratio λ (=1/Kaf), thefinal EGR rate calculation unit 72 calculates the reciprocal of the fuelcorrection coefficient Kaf.

Alternatively, it may be allowed that based on a control mode for theair-fuel ratio, the final EGR rate calculation unit 72 determineswhether the air-fuel ratio AF is rich, lean, or the theoretical air-fuelratio, and sets the excess air ratio λ. The control modes for theair-fuel ratio include a theoretical air-fuel ratio control mode, a richcontrol mode, and a lean control mode. In the theoretical air-fuel ratiocontrol mode, in order to raise the purification performance of thethree-way catalyst, the air-fuel ratio AF detected by the air-fuel ratiosensor 18 is feedback-controlled so as to be in the vicinity of thetheoretical air-fuel ratio AF0. In the rich control mode, which is setat a time when high-load driving is performed, the air-fuel ratio AF iscontrolled so as to be rich. In the lean control mode, which is set, forexample, in order to raise the gasoline mileage, the air-fuel ratio AFis controlled so as to be lean. In the case where the control mode forthe air-fuel ratio is the theoretical air-fuel ratio control mode, therich control mode, or the lean control mode, the final EGR ratecalculation unit 72 determines that the air-fuel ratio is thetheoretical air-fuel ratio, rich, or lean, as the case may be. Asdescribed above, the final EGR rate calculation unit 72 calculates theexcess air ratio λ, based on the detection value of the air-fuel ratioAF, detected by the air-fuel ratio sensor 18, or the fuel correctioncoefficient Kaf.

3. Embodiment 3

Next, the controller 50 according to Embodiment 3 will be explained. Theexplanation for constituent parts the same as those in each ofEmbodiments 1 and 2 will be omitted. The respective basic configurationsand processing methods of the internal combustion engine 1 and thecontroller 50 according to Embodiment 3 are the same as those of theinternal combustion engine 1 and the controller 50 according to each ofEmbodiments 1 and 2; however, Embodiment 3 is different from each ofEmbodiments 1 and 2 in that the intake-air humidity sensor 5 is notprovided in the internal combustion engine 1 and is also different inthe detection methods for the intake-air pressure Pa, the intake-airtemperature Ta, and the intake-air humidity Hra.

In each of Embodiments 1 and 2, there has been explained the case wherethe driving-condition detection unit 51 detects the intake-air pressurePa, based on the output signal of the intake-air pressure sensor 2,detects the intake-air temperature Ta, based on the output signal of theintake-air temperature sensor 4, and detects the intake-air humidityHra, based on the output signal of the intake-air humidity sensor 5.

However, in Embodiment 3, as the intake-air pressure Pa, the intake-airhumidity Hra, and the intake-air temperature Ta, the driving-conditiondetection unit 51 detects the manifold pressure Pb, the manifoldhumidity Hrb, and the manifold temperature Tb, respectively, under thecondition that the EGR valve 22 for opening closing the EGR path 21 isclosed and hence no exhaust gas is recirculated to the intake manifold12.

In Embodiment 3, in the case where the EGR valve 22 has continuouslybeen closed for a preliminarily set determination period, thedriving-condition detection unit 51 determines that an intake airdetection condition has been satisfied. The determination period is setto a period in which after the EGR valve 22 is closed, recirculationexhaust gas in the intake manifold 12 sufficiently decreases. Thedetermination period may be shortened as the intake air amountincreases. While the intake air detection condition is satisfied, thedriving-condition detection unit 51 detects the intake-air pressure Pa,based on the output signal of the manifold pressure sensor 8, detectsthe intake-air temperature Ta, based on the output signal of themanifold temperature sensor 9, and detects the intake-air humidity Hra,based on the output signal of the manifold humidity sensor 10. While theEGR valve 22 is closed, no exhaust gas is recirculated into the intakemanifold 12; thus, only intake air exists therein. As a result, by useof the pressure, the humidity, and the temperature of the gas in theintake manifold 12, that are detected under the foregoing condition, theinner-intake-air water vapor partial pressure Pva and theinner-intake-air water vapor partial pressure ratio (Pva/Pa) can becalculated.

As is the case with Embodiment 1, based on the intake-air humidity Hraand the intake-air temperature Ta that are detected at a time when theintake air detection condition is satisfied, the inner-intake-air watervapor ratio calculation unit 71 calculates the partial pressure Pva ofinner-intake-air water vapor, which is the partial pressure of watervapor included in the intake air, so as to calculate theinner-intake-air water vapor partial pressure ratio (Pva/Pa), which isthe ratio of the partial pressure Pva of the inner-intake-air watervapor to the intake-air pressure Pa. When the intake air detectioncondition is not satisfied, the inner-intake-air water vapor ratiocalculation unit 71 holds and outputs the inner-intake-air water vaporpartial pressure ratio (Pva/Pa) that has been calculated at a time whenthe intake air detection condition was satisfied. The humidity ofatmospheric air changes more gently than the humidity in the intakemanifold 12 changes due to a change in the EGR rate; therefore, evenwhen the held value is utilized, a large estimation error is preventedfrom occurring in the EGR rate.

OTHER EMBODIMENTS

Lastly, other embodiments of the present invention will be explained.Each of the configurations of embodiments to be explained below is notlimited to be separately utilized but can be utilized in combinationwith the configurations of other embodiments as long as no discrepancyoccurs.

(1) In each of the foregoing embodiments, there has been explained thecase in which considering the case where as the fuel for the internalcombustion engine 1, gasoline is utilized, it is assumed that theaverage molecular formula of gasoline and the composition of air aregiven by each of the equations (14), (32), and (35). However,embodiments of the present invention are not limited to the foregoingcase. In other words, it may be allowed that in the average molecularformula of gasoline and the composition of air, stricter values areutilized, that the chemical reaction formula and the respective numbersof moles of molecules in the chemical reaction formula are changed, andthat the setting values for calculating the humidity detecting EGR rateRegr such as the conversion constant Kr and the mole conversion constantKr2 are changed. Moreover, it may be allowed that as the fuel of theinternal combustion engine 1, for example, light oil, alcohol, naturalgas, or the like is utilized, that the average molecular formula of thefuel is changed in accordance with the kind of the fuel, that thechemical reaction formula and the respective numbers of moles ofmolecules in the chemical reaction formula are changed, and that thesetting values for calculating the humidity detecting EGR rate Regr suchas the conversion constant Kr and the mole conversion constant Kr2 arechanged.

(2) In each of the foregoing embodiments, there has been explained thecase in which the driving-condition detection unit 51 detects theintake-air temperature Ta, based on the output signal of the intake-airtemperature sensor 4, and detects the intake-air humidity Hra, based onthe output signal of the intake-air humidity sensor 5. However,embodiments of the present invention are not limited to the foregoingcase. That is to say, it may be allowed that the driving-conditiondetection unit 51 obtains information on the intake-air humidity Hra andthe intake-air temperature Ta from the air conditioner controller 80.The air conditioner controller 80 is a controller for an air conditionerthat performs air-conditioning of a vehicle interior and is connectedwith the controller 50 for the internal combustion engine 1 through acommunication wire. The air conditioner controller 80 is provided with ahumidity sensor that detects the humidity of atmospheric air to be takeninto the air conditioner and a temperature sensor that detects thetemperature of atmospheric air, detects the atmospheric-air humidity andthe atmospheric-air temperature based on the output signals of thehumidity sensor and the temperature sensor, and transmits information onthe atmospheric-air humidity and the atmospheric-air temperature to thecontroller 50.

(3) In each of the foregoing embodiments, there has been explained thecase in which the recirculation amount utilization control unit 55performs, as mentioned above, at least one or more of a change of theignition timing, a change of the opening degree Oe of the EGR valve 22,and a calculation of an output torque of the internal combustion engine1, based on the flow rate Qes of the recirculation exhaust gas forcontrol. However, embodiments of the present invention are not limitedto the foregoing case. That is to say, it may be allowed that therecirculation amount utilization control unit 55 uses the recirculationexhaust gas flow rate Qes for control of other than these controls, forexample, a control of the intake air amount, a control for changing thevalve opening and closing timing of one or both of the intake valve 14and the exhaust valve 15, and the like.

Various modifications and alterations of this invention will be apparentto those skilled in the art without departing from the scope and spiritof this invention, and it should be understood that this is not limitedto the illustrative embodiments set forth herein.

What is claimed is:
 1. A controller for an internal combustion enginethat is provided with an intake path and an exhaust path, a throttlevalve for opening and closing the intake path, an EGR path forrecirculating exhaust gas from the exhaust path to an intake manifoldthat is part of the intake path and is at the downstream side of thethrottle valve, and an EGR valve for opening and closing the EGR path,the controller for the internal combustion engine comprising: adriving-condition detector that detects a manifold pressure, which is apressure of gas in the intake manifold, a manifold temperature, which isa temperature of gas in the intake manifold, a manifold humidity, whichis a humidity of gas in the intake manifold, an intake-air pressure,which is a pressure of intake air to be taken into the intake path, anintake-air temperature, which is a temperature of the intake air, anintake-air humidity, which is a humidity of the intake air, an intakeair flow rate, which is a flow rate of the intake air, and an openingdegree of the EGR valve; a humidity detecting EGR rate calculator thatcalculates a humidity detecting EGR rate, which is a ratio of arecirculation exhaust gas, which is the exhaust gas recirculated intothe intake manifold, to the intake air, based on the intake-airtemperature, the intake-air humidity, the intake-air pressure, themanifold temperature, the manifold humidity, and the manifold pressure;an opening area learning value calculator that calculates a humiditydetecting recirculation flow rate which is a flow rate of therecirculation exhaust gas based on the humidity detecting EGR rate andthe intake air flow rate, calculates a humidity detecting opening area,which is an opening area of the EGR valve which realizes the humiditydetecting recirculation flow rate, and calculates a learning value ofthe opening area of the EGR valve based on the humidity detectingopening area; and a recirculation exhaust gas calculator for controlthat calculates a learned opening area of the EGR valve corresponding tothe present opening degree of the EGR valve using the learning value ofthe opening area, and calculates a flow rate of the recirculationexhaust gas for control used for controlling the internal combustionengine based on the learned opening area.
 2. The controller for theinternal combustion engine according to claim 1, wherein thedriving-condition detector detects a temperature of the exhaust gas atthe exhaust path side of the EGR valve, and a pressure of the exhaustgas at the exhaust path side of the EGR valve, wherein the opening arealearning value calculator calculates a sonic velocity of the exhaust gasat the exhaust path side of the EGR valve based on the temperature ofthe exhaust gas, calculates a density of the exhaust gas at the exhaustpath side of the EGR valve based on the temperature of the exhaust gasand the pressure of the exhaust gas, and calculates the humiditydetecting opening area based on the manifold pressure, the pressure ofthe exhaust gas, the sonic velocity of the exhaust gas, the density ofthe exhaust gas, and the humidity detecting recirculation flow rate. 3.The controller for the internal combustion engine according to claim 2,wherein the opening area learning value calculator calculates a baseopening area corresponding to the present opening degree of the EGRvalve, by use of a base opening characteristic data in which therelationship between the base opening area of the EGR valve and theopening degree of the EGR valve is preliminarily set, and calculates thelearning value of the opening area based on the comparison resultbetween the base opening area and the humidity detecting opening area,wherein the recirculation exhaust gas calculator for control calculatesthe learned opening area by correcting the base opening area with thelearning value of the opening area, and calculates the flow rate of therecirculation exhaust gas for control based on the learned opening area,the manifold pressure, the pressure of the exhaust gas, the sonicvelocity of the exhaust gas, and the density of the exhaust gas.
 4. Thecontroller for the internal combustion engine according to claim 1,wherein the opening area learning value calculator calculates thelearning value of the opening area for each operating point of theopening degree of the EGR valve, the recirculation exhaust gascalculator for control calculates the flow rate of the recirculationexhaust gas for control using the learning value of the opening areacorresponding to the present opening degree of the EGR valve.
 5. Thecontroller for the internal combustion engine according to claim 1,wherein the opening area learning value calculator permits a update ofthe learning value of the opening area in the case of determining that achange of the EGR rate is small and in a steady state, and prohibits theupdate of the learning value of the opening area and holds the learningvalue of the opening area in the case of determining that the change ofthe EGR rate is large and in a transient state.
 6. The controller forthe internal combustion engine according to claim 1, further comprising:a recirculation amount utilization controller performs at least one ormore of a calculation of an output torque of the internal combustionengine, a change of an ignition timing, and a change of the openingdegree of the EGR valve, based on the flow rate of the recirculationexhaust gas for control.
 7. The controller for the internal combustionengine according to claim 1, the humidity detecting EGR rate calculatorincludes: an inner-manifold water vapor ratio calculator that calculatesan inner-manifold water vapor partial pressure, which is a partialpressure of water vapor included in gas inside the intake manifold,based on the manifold humidity and the manifold temperature, andcalculates an inner-manifold water vapor partial pressure ratio, whichis the ratio of the inner-manifold water vapor partial pressure to themanifold pressure; an inner-intake-air water vapor ratio calculator thatcalculates an inner-intake-air water vapor partial pressure, which is apartial pressure of water vapor included in the intake air, based on theintake-air humidity and the intake-air temperature, and calculates aninner-intake-air water vapor partial pressure ratio, which is the ratioof the inner-intake-air water vapor partial pressure to the intake-airpressure; and a final EGR rate calculator that calculates the humiditydetecting EGR rate based on the inner-manifold water vapor partialpressure ratio and the inner-intake-air water vapor partial pressureratio.
 8. The controller for the internal combustion engine according toclaim 7, wherein the final EGR rate calculator calculates a subtractionpartial pressure ratio by subtracting the inner-intake-air water vaporpartial pressure ratio from the inner-manifold water vapor partialpressure ratio, multiplies the subtraction partial pressure ratio by apreliminarily set conversion constant, and then calculates, as thehumidity detecting EGR rate, a value by dividing the multiplicationvalue by a subtraction value obtained by subtracting theinner-intake-air water vapor partial pressure ratio from “1”.
 9. Thecontroller for the internal combustion engine according to claim 7,wherein the final EGR rate calculator calculates an inner-manifoldcombustion-produced water vapor partial pressure ratio, which is a ratioof the partial pressure of combustion-produced water vapor included inthe recirculated exhaust gas to the manifold pressure, by subtractingthe inner-intake-air water vapor partial pressure ratio from theinner-manifold water vapor partial pressure ratio; based on therespective numbers of moles of molecules in a chemical reaction formulaat a time when a fuel and wet air combust together and theinner-intake-air water vapor partial pressure ratio, the final EGR ratecalculator calculates an inner-exhaust-gas combustion-produced watervapor mole fraction, which is a mole fraction of combustion-producedwater vapor in the exhaust gas; then, the final EGR rate calculatorcalculates, as the humidity detecting EGR rate, a value by dividing theinner-manifold combustion-produced water vapor partial pressure ratio bythe inner-exhaust-gas combustion-produced water vapor mole fraction. 10.The controller for the internal combustion engine according to claim 7,wherein the final EGR rate calculator changes the humidity detecting EGRrate in accordance with an air-fuel ratio of the internal combustionengine.
 11. The controller for the internal combustion engine accordingto claim 7, wherein the final EGR rate calculator calculates thehumidity detecting EGR rate at a time when it is assumed that anair-fuel ratio of the internal combustion engine is a theoreticalair-fuel ratio, based on the inner-manifold water vapor partial pressureratio and the inner-intake-air water vapor partial pressure ratio; inthe case where the air-fuel ratio is leaner than the theoreticalair-fuel ratio, the final EGR rate calculator calculates, as the finalhumidity detecting EGR rate, a value by multiplying the humiditydetecting EGR rate at a time when it is assumed that the air-fuel ratiois the theoretical air-fuel ratio by an excess air ratio obtained bydividing the air-fuel ratio by the theoretical air-fuel ratio; in thecase where the air-fuel ratio is richer than the theoretical air-fuelratio, the final EGR rate calculator directly calculates, as the finalhumidity detecting EGR rate, the humidity detecting EGR rate at a timewhen it is assumed that the air-fuel ratio is the theoretical air-fuelratio.
 12. The controller for the internal combustion engine accordingto claim 1, wherein as the intake-air pressure, the intake-air humidity,and the intake-air temperature, the driving-condition detector detectsthe manifold pressure, the manifold humidity, and the manifoldtemperature under the condition that the EGR valve for the path isclosed and hence no exhaust gas is recirculated to the intake manifold.13. The controller for the internal combustion engine according to claim1, wherein the driving-condition detector obtains information on theintake-air humidity and the intake-air temperature from an airconditioner controller.
 14. A control method for an internal combustionengine that is provided with an intake path and an exhaust path, athrottle valve for opening and closing the intake path, an EGR path forrecirculating exhaust gas from the exhaust path to an intake manifoldthat is part of the intake path and is at the downstream side of thethrottle valve, and an EGR valve for opening and closing the EGR path,the control method comprising: a driving-condition detecting thatdetects a manifold pressure, which is a pressure of gas in the intakemanifold, a manifold temperature, which is a temperature of gas in theintake manifold, a manifold humidity, which is a humidity of gas in theintake manifold, an intake-air pressure, which is a pressure of intakeair to be taken into the intake path, an intake-air temperature, whichis a temperature of the intake air, an intake-air humidity, which is ahumidity of the intake air, an intake air flow rate, which is a flowrate of the intake air, and an opening degree of the EGR valve; ahumidity detecting EGR rate calculating that calculates a humiditydetecting EGR rate, which is a ratio of a recirculation exhaust gas,which is the exhaust gas recirculated into the intake manifold, to theintake air, based on the intake-air temperature, the intake-airhumidity, the intake-air pressure, the manifold temperature, themanifold humidity, and the manifold pressure; an opening area learningvalue calculating that calculates a humidity detecting recirculationflow rate which is a flow rate of the recirculation exhaust gas based onthe humidity detecting EGR rate and the intake air flow rate,calculating a humidity detecting opening area, which is an opening areaof the EGR valve which realizes the humidity detecting recirculationflow rate, and calculates a learning value of the opening area of theEGR valve based on the humidity detecting opening area; and arecirculation exhaust gas calculating for control that calculates alearned opening area of the EGR valve corresponding to the presentopening degree of the EGR valve using the learning value of the openingarea, and calculates a flow rate of the recirculation exhaust gas forcontrol used for controlling the internal combustion engine based on thelearned opening area.